A world which has a lot of water and is within the temperature range for liquid water should have water vapor in the atmosphere.
On Earth the ozone layer absorbs deadly ultraviolet radiation from the Sun. The ozone layer is in the stratosphere which begins at about 6 to 20 kilometers and goes up to about 50 kilometers.
So the upper atmosphere above the stratosphere - the Mesosphere, and thermosphere, and exosphere - is exposed to the ultraviolet radiation from the Sun and unprotected from it.
So if there is water vapor in the atmosphere of an alien world, ultraviolet radiation will split up some molecules of water into atoms of hydrogen and oxygen. And most of the time atoms of hydrogen and oxygen will recombine to form water vapor again. But some of the oxygen will form oxygen molecules and some of the hydrogen will rise, being the lightest gas.
Here is a link to an article discussing the possible abiotic production of oxygen in the atmospheres of various worlds.
https://iopscience.iop.org/article/10.3847/1538-4357/aaca36
Some of the hydrogen will rise to the exosphere and to the escape layers of the atmosphere. The gases in Earth's exosphere are heated a lot by the ultraviolet radiation from the Sun. Earth has a surface temperature of about 288 Kelvin, but gases in the exosphere have temperatures in the range of 1,000 to 2,000 K. The hotter a gas is, the faster its particles move. The lighter a gas is, the faster it moves at a specific temperature. So the hydrogen atoms and molecules in the exosphere of Earth escape much more rapidly than the atoms and molecules of oxygen in the exosphere.
Naturally you would want the escape velocity of such a world to be as low as possible for hydrogen to escape as fast as possible - while still being high enough to retain oxygen for long times - to produce an oxygen atmosphere out of a water vapor one as fast as possible, so that the addition of oxygen will be faster than its loss by forming solid compounds and falling to the ground.
Earth has an escape velocity of 11.186 kilometers per second. According to Stephen H. Dole, Habitable Planets for Man (1964) page 54.
https://www.rand.org/content/dam/rand/pubs/commercial_books/2007/RAND_CB179-1.pdf
If a planet could have surface temperatures warm enough for humans and also exosphere temperatures never exceeding 1000 degrees Kelvin, it would need an escape velocity of only 6.25 kilometers per second - 5 times the root-mean-square velocity of atomic oxygen at 1000 degrees Kelvin - to retain an oxygen atmosphere for a long time.
To be specific, according to table 5 on page 35, if the ratio o a world's escape velocity divided by the root-mean-square velocity of a gas at the exosphere temperature is five, the world will retain 0.368 of the original amount of the gas after about 100 million years. And it is quite possible that the gas might be replaced from various sources about as fast as it is lost, if the loss rate is that slow.
Dole had a formula for calculating the relationship between the mass and radius, and thus surface gravity and escape velocity, of a terrestrial type planet, with results displayed in figure - on page 31. But I guess that Dole's formula is probably somewhat obsolete after 60years, with all the more accurate data point about the worlds in our solar system now available, as well as some data about extrasolar planets.
Anyway, on page 54 Dole used that formula to deduce that a world with an escape velocity of 6.25 kilometers per second (0.5587 that of Earth) would have a mass of 0.195 Earth Mass, a radius of 0.63 Earth radius (& thus 4,013.73 Kilometers), and a surface gravity of 0.49 g. Note that all these parameters of that hypothetical world have different ratios compared to the values for Earth. One must especially beware of assuming that the surface gravity and the escape velocity will have the same ratio compared to Earth's values.
Dole decided that even though that world could retain an oxygen rich atmosphere for long eras of time, it was too small to produce a dense atmosphere. On page 56 to 57, Dole decided that the smallest world capable of producing a dense atmosphere would have a mass of about 0.40 that of Earth, with a radius of 0.78 Earth radius (and thus 4,969.38eters), and a surface gravity of 0.68 g. And I can add an escape velocity of 8.01 kilometers per second (0.716 of Earth's escape velocity).
But I think that Dole was proved wrong in his belief that a world smaller than that could not produce a dense atmosphere. Decades later, shocking facts were discovered about Titan, the largest moon of Saturn.
Titan has a radius of 2,574.73 kilometers (0.404 that of Earth), a mass 0.0225 that of Earth, a surface gravity 0.138 that of Earth, and an escape velocity of 2.641 kilometers per second (0.236 that of Earth).
Observations from the Voyager space probes have shown that Titan's atmosphere is denser than Earth's, with a surface pressure about 1.45 atm. It is also about 1.19 times as massive as Earth's overall,[44] or about 7.3 times more massive on a per surface area basis.
https://en.wikipedia.org/wiki/Titan_(moon)#Atmosphere
Titan is able to retain its atmosphere for a long time despite its low escape velocity, because it is very cold and gases in its exosphere have much lower velocities than on Earth.
But the fact that Titan ever formed such a dense atmosphere gives hope that Dole was wrong about the minimum size of a world capable of forming a dense atmosphere. Maybe a world with only 0.195 the mass of Earth could retain an atmosphere for a long time. Maybe even a smaller one.
On pages 3 to 4 of this 2013 article:
https://www.google.com/search?q=exomoon+habitability+constrained+by+illumination+and+tidal+heating+pdf&oq=&aqs=chrome.3.69i57j46i67i131i433i650j69i59l2j35i39j69i60l3.7079j0j7&sourceid=chrome&ie=UTF-8
There is a discussion of the mass range of a world habitable for liquid water using life in general (not necessarily for humans in particular).
A minimum mass of an exomoon is required to drive a magnetic shield on a billion-year timescale (Ms ≳ 0.1M⊕,
Tachinami et al. 2011); to sustain a substantial, long-lived atmosphere (Ms ≳ 0.12M⊕, Williams et al. 1997; Kaltenegger
2000); and to drive tectonic activity (Ms ≳ 0.23M⊕, Williams et al. 1997), which is necessary to maintain plate tectonics and
to support the carbon-silicate cycle. Weak internal dynamos have been detected in Mercury and Ganymede (Kivelson et al.
1996; Gurnett et al. 1996), suggesting that satellite masses > 0.25M⊕ will be adequate for considerations of exomoon
habitability. This lower limit, however, is not a fixed number. Further sources of energy – such as radiogenic and tidal
heating, and the effect of a moon’s composition and structure – can alter our limit in either direction.
https://arxiv.org/ftp/arxiv/papers/1209/1209.5323.pdf
So it claims that a minimum mass of at least 0.12 Earth is necessary for a world to retain a substantial, long-lived atmosphere.
Assuming that a world with 0.12 the mass of Earth has the density of the Moon, it would 0.5525 the radius of Earth (and thus 3,556 Kilometers) and an escape velocity of 5.186 kilometers per second (0.4636 that of Earth).
Assuming that a world with 0.12 the mass of Earth has the density of Mars, it would 0.55202 the radius of Earth (and thus 3,516.9 Kilometers) and an escape velocity of 5.215 kilometers per second (0.4662 that of Earth).
It is possible that worlds with masses as low as 0.12 Earth can't retain oxygen, but can retain heavier gases enough to have sufficient pressure to maintain liquid water on the surface.
In any case, a world with an escape velocity as low as 6.25 kilometers per second, or maybe even 5.0 kilometers per second, might retain oxygen for a long time while rapidly losing hydrogen produced by ultraviolet light breaking up molecules of water.
You might want your world to be a water would, with a world wide ocean many kilometers deep covering all the land. It is possible that the exotic temperatures and pressures at the bottom of the ocean might slow down the interactions between oxygen dissolved in the water and the solid matter at the bottom of the ocean, thus reducing the rate at which oxygen is removed from the atmosphere.
Or you might want your world to have a lot of land surface, but a lot of the land surface might be covered with ice and snow.
Water vapor is a strong greenhouse gas. But if your world's atmosphere originally has 10 or 20 percent water vapor, almost all of that would have to be broken up into oxygen and hydrogen, and the hydrogen lost.
According to table 4 on page 21 of Habitable Planets for Man humans can tolerate up to 25 millimeters of mercury pressure of water vapor, depending on the temperature. Earth's atmosphere at sea level has a total pressure of 760 millimeters of mercury, thus making the maximum water vapor about 3.2 percent of the atmosphere.
So most of the water vapor would have to be taken out of the atmosphere and its greenhouse effect would be greatly reduced, lowering the temperatures on your world. That decrease in temperature might be enough to freeze over most of the oceans with pack ice and for glaciers to cover most of the land of the planet. That would reduce the area where oxygen in the atmosphere could react with ground and rock to be taken out of the atmosphere.
Another possibility is that your world had life for billions of years and those lifeforms produced an oxygen rich atmosphere after billions of years, and then all life on the world was ended.
for example, a direct hit by the beam from a gamma ray burster would destroy the ozone layer which would permit ultraviolet rays to reach the surface. The ultraviolet rays would kill all life on land and all life at the surface of he ocean. Only bacteria inside rocks and lifeforms by deepsea vents could survive.
And it would take many thousands or millions of years for oxygen in the atmosphere to interact with other matter and form solid oxygen compounds on the ground. And maybe the continuing ultraviolet radiation would break up water vapor molecules to partially replace the oxygen. So if humans visit that world soon enough after the gamma ray burst struck, there would still be an oxygen rich atmosphere despite the lack of plant life to maintain it for geological ages.