TV tropes has a trope about the hardness of science fiction. BMF should ask themself how "hard" they want their story to be.
Here is a frame challenge:
Can a world with a surface gravity of only 3.34 meters per second per second have an atmospheric presssure of 101,325 Pa, or one Earth atmosphere?
Earth has a surface gravity of 9.80665 meters per second per second (1 g), and a sea level atmospheric pressure of 101,325 Pa, or one Earth atmosphere. So your world has a surface gravity of 0.34 g.
Actually the amount of time that a world can retain whatever atmosphere it may produce or acquire depends primarily on its escape velocity, and not on its surface gravity. Since the escape velocity of a world is calculated using a different formula than its surface gravity, the diiference in surface gravity between two worlds will usually not be the same as the difference in their escape velocities.
I note that Mars, and Mercury, have low surface gravities and atmospheres much less dense than 1 Earth Atmosphere.
Mars has a surface gravity of 3.72076 meters per second per second (0.379 g), and Mercury has a surface gravity of 3.7 meters per second per second (0.377 g). Both are somewhat more than your desired world with 0.34 g.
The escape velocity of Earth is 11.186 kilometers per second. The escape velocity of Mars is 5.027 kilometers per second (0.449 that of Earth) and Mercury's is 4.25 kilometers per second (0.349 that of Earth). In those cases Mars has a higher relative escape velocity than surface gravity, and Mercury has a lower relative escape velocity than surface gravity.
So it is possible to design a planet with an escape velocity relatively higher than its surface gravity.
Habitable planets for Man Stephen H. Dole, 1964, discusses the escape velocity necessary for a planet to retain a dense atmosphere for geological eras of time and for oxygen to accumulate in its atmosphere.
Planets lose atmosphere when it either combines with other materials to be come solid instead of gas, or escapes into outer space. Gases escape into space from the topmost layers of the palntary atsmsphere, their exospheres, where gases are very thin and very hot. The temperatures in the exospheres of worlds are usually several times the temperatures at the sufaces of the worlds. And of course the hotter the gas particles are, the faster they move, and the more likely they are to move faster than the escape velocity of their world and so be lost into space.
ONpages 34 and 35 Dole discusses the ratio between the planetary escape velocity and the root-mean-square velocity of a gas in the exosphere. How long it takes the original amount of that gas in the atmosphere to be reduce to 1/e, or 0.3678796 of the original amount. depends on the ratio of the escape velocity divided by the root-mean-square of the gas's exosphere velocity.
Table 5 on page 35 shows that if the ratio is 1 or 2, the time to reduce the atmosphere by that amount is zero.
If the ratio is 3, the time to reduce the atmosphere is a few weeks.
If the ratio is 4, the time to reduce the atmosphere is several thousand years.
If the ratio is 5, the time to reduce the atmosphere is about ahundred million years.
If the ratio is 9, the time to reduce the atmosphere is approximately infinite.
Thus a comparatively minor change in the ratio between the escape velocity of a world and the root-mean-square of gas in its exosphere can make the difference between the planet loosing all its atmosphere almost instantly and retaining its atmosphere almost infinitely.
Of course in some cases atmospheric gaess can be replaced by sources on the planet as fast as they are lost into space. But obviously it would be a lot more probable for natural forces to replace atmosphere as fast as it is lost if it takes 100 million years for the atmosphere to be reduced to 0.3678 of its orginal amount than if it takes only 100 million seconds or about 3.2 years.
And the stellar wind can cause a planet to lose atmosphere if the planet doesn't have a magnetosphere to divert charged particles away from the exosphere.
But the escape velocity is much more important.
On page 54 Dole noted that the temperatures in Earth's exosphere are between 1000 K and 2000 K. Dole said that if the temperaturs in the exosphere of a planet never exceedes 1000 K, and the planetary surface is still warm enough for liquid water, a planet could retain a long term oxygen rich atmosphere if its escpe velocity was at least 6.25 kilometers per second (5 times 1.25 kilometes per second).
According to Dole's figures, based on his formula for relating the mass, density,a nd radius of a planet, a planet with an escape vleocity of 6.25 kilometer per second would have a mass 0.195 that of Earth, a radius of f.63 Earth radius, and a surface gravity of 0.49 g, considerably higher than the 0.34 g you desire.
If there can be considerable variation in the overall density of a habitable planet, it might be possible to design a planet which as a surface gravity as low as 3.34meters per second per second (0.34 g), and an escape velocity as high as 6.25 kilometers per second, 0.5587 that of Earth.
But there are limitations to how high or low you can make the average density of a planet which has a solid surface partially covered by oceans and partially above the oceans, as on Earth.
Earth has an average density of 5.514 grams per cubic centimeter.
Our solar system was four terrestrial type planets, of which Earth is the densest, and four giant planets which are largely composed of hydrogen and helium gases and so have low average densities.
Neptune has the highest average density of the known giant planets, at 1.638 grams per cubic centimeter, 0.297062 that of Earth. And Neptune doesn't have anything like a solid surface.
imagine a world with the same average density as Neptune but the same mass as Earth. To have the same mass as Earth with 0.297062 the density it woudl have to have 3.3663006 times the volume of Earth. 1.49872 is the cube root of 3.3663673, which is close enough. Since the average radius of Earth is 6,671.0 kilometers, the average radius of such a planet would be about 9,548.3451 kilometers.
According to this online surface gravity calculator:
The planet would have a surface gravity of 0.45 g, higher than you desire.
According to this online escape velocity calculator, the planet would have an escape velocity of 9.137 kilometers per second, about 0.8168 that of Earth.
Suppose that a planet has an average density of about 2.757 grams percubic centimeter, about half that of Earth. If such a planet had the mass of Earth, it would have twice the volume of Earth. Since 1.26 is the cube root of 2.00376, that is close enough. That planet would have a radius of about 8,027.46 kilometers.
Such a planet would have a surface gravity of 0.63 g, and an escape velocity of 9.965 kilometers per second.
So it looks like you need to use a planet less dense. But I am not sure that a world less dense than that could exist without having a lot of liquid, enough liquid that its solid surface would be covered by hundreds of kilometers or miles of liquid. If you want native land dwelling people on that planet to build boatsout of wood from trees on land, that would be no good.
There have been a number of other posts in various places where I have tried to calculate worlds which surface gravities as low as possible and escape velocities high enough to retain atmospheres for billions of years.
And maybe I can link to them.
Part Two: A titanic solution.
There is a world in our solar system which has an atmmosphereic surface pressure even higher than that of Earth, despite having a very low escape velocity, much lower than an habitable world should have. It is Titan, the largest moon of Saturn. Titan receives only about 1 percent as much energy from the Sun as Earth does, so it is much colder in Titan's exosphere than in Earth's exposphere, so Titan's low escape velocity of 2.639 kilometersper second, 0.2359 that of Earth, is enough to retain its atmosphere.
Of coure that means the surface of Titan is very cold, so water is frozen rock hard. The temperaturea and pessure on Titan is near the triple point of methane, so methan can be, and is, solid, liquid, and gaseous on Titan. Titan is believed to have many methane lakes of various sizes; The largest, Kraken Mare, is about 900 kilometers long, and even the smallest known ones are large enough for boating.
I note that the surface gravity of Titan is 0.632 kilometers per second per second, less than you desire, and that liquid methane may have different properties than liquid water. But hums owuld able to survive on Titan with breathing apparatus and temperature suits, and it might possibly be that their are lifeforms on Titan and/or similar worlds in other star systems, lifeforms which use liquid methane as their solvant instead of liquid water.
Part Three: The smallest possible habitable worlds.
Since Earth type life forms use liquid water, and liquid water requires a dense anough atmosphere, a planet has to be able to retain a dense enough atmospehre for geological eras of time to retain liquid water and thus have water oceans and lakes for the life forms. And you also want a planet with water oceans and lakes to sail on.
Recently some scientists have imagined how some types of planets could retain atmosphere andthus liquid water despite having much lower mass and escape velocity than previously believed.
Under some conditions, a planet as small as 0.0268 Earth mass could retain an atmosphere and liquid water for geological eras of time, according to their calculations.
But what's the difference from worlds used in earlier calculations, and what is the catch?
The discussion is about water worlds of low mass.
The orginal article: https://iopscience.iop.org/article/10.3847/1538-4357/ab2bf2
We assume that the low-gravity waterworld has a pure water vapor atmosphere and a water reservoir fixed at 40% of the planet's total mass.
So the solid surfaces of those planet and moons are likely to be at the bottoms of oceans hundreds or thousands of kilometers deep. Such planets would not have native land dwelling intelligent beings to build boats out of wood, and there wouldn't be any trees to build old fashioned boats out of.
But space travelers from other worlds could bring their own boats and ships to such worlds to sail in their oceans. The study assumed that the atmospheres would be all water vapor from the oceans.
But ultaviolent light would beak up water vapor molecules into hydrogen and oxygen atoms. The hydrogen atoms would escape much faster than the oxygen atoms, so oxygen might accululate in the atmosphere and which might eventually become breathable.
And possibly the oceans of that world might develop floating islands of some type where land plants and animals might evolve, possibly including people who make baot sout of tree equivalents.
Part Four: Worlds With Roofs.
A world which has too low an escape velocity to retain an atmosphere naturally might be terraformed to have an artificial atmosphere and the terraformers might put a roof over the world to hold the atmosphere in.
There are several different hypothetical types of "shellworld" maegastructures. Two theoretical types of shellworlds are:
An inflated canopy holding high pressure air around an otherwise airless world to create a breathable atmosphere.5 The pressure of the contained air supports the weight of the shell.
Completely hollow shell worlds can also be created on a planetary or larger scale by contained gas alone, also called bubbleworlds or gravitational balloons, as long as the outward pressure from the contained gas balances the gravitational contraction of the entire structure, resulting in no net force on the shell. The scale is limited only by the mass of gas enclosed; the shell can be made of any mundane material. The shell can have an additional atmosphere on the outside.
The first type of shell world could have lakes and oceans on its surfice beneath the shell, while the second type could have water as well as atmosphere within its shell. Enough mass of water would form a sphere surrounded by the gas.
Part Five: Conclusion.
Asking for a world with surface water to sail on, an Earth like atmosphere, and a surface gravity of 3.34 meters pr second per second, causes some problems in designing the world which the OP didn't anticipate.
I hope that my suggested solutions to the problems will be helpful.