The planetary orbits you propose might be possible.
The problem you have to consider is that a naturally habitable planet should have existed with relatively constant orbital parameters and relatively constant heat and light from its star for a very long time. Earth didn't become habitable for humans for billions of years after it formed.
There is no problem designing a solar system where all the planets are uninhabitable for humans, or where none of the planets have advanced multi celled life forms, or intelligent natives, or any of the stuff that makes most science fiction planets interesting. You don't have to worry about the parameters since there are so many different ways for a planet to be dead and uninhabitable.
Having twelve planets beyond the habitable zone and too cold for life is perfectly plausible.
The habitable zone seems to stretch from the 97th orbit or inwards of it to the 108th orbit. Thus there are least 12 planets in the habitable zone, ten with toxic atmospheres and two habitable ones. The habitable zone could include planets inwards of the 97th orbit.
But having up to 96 planets closer to the star than the inner edge of the habitable zone is a bit of a problem.
Astronomers are in doubt whether the Sun's habitable zone includes, one, two, or three planetary orbits. If Mars and/or Venus are with in the Sun's habitable zone other factors make them uninhabitable. Only one planet in the Solar system, Earth, is habitable, which means that astronomers can't be certain which other planets are within the Sun's habitable zone.
But the two inner planets, Mercury and Venus, are known to be too hot for humans, and the four outermost planets, Jupiter, Saturn, Uranus, and Neptune, and all former planets, dwarf planets, etc. are known to be too cold. If Mars was big enough to hold onto more air and water it might be habitable.
Thus in our solar system, planets too hot to be habitable are outnumbered at least two to one by planets too cold to be habitable, and that makes sense, because nice and warm planets have to be close enough to the star, too hot planets have to be even closer, and planets that are too cold can orbit farther and father away from the star, each farther planet getting colder and colder and colder, out to some vast distance.
So I find it easier to believe in a star system with 120 planets where 12 are too hot, 12 are in the habitable zone and some of them are habitable, and 96 are too cold, than in your system, where 12 planets are too cold, 12 are in the habitable zone (& 2 of them habitable), and 96 are too hot.
I don't know what the story reasons are for for having so many uninhabitable planets in your system, nor for making most of the uninhabitable planets too hot instead of too cold. So I don't know if it would be good for your story to switch the numbers of too hot planets and too cold planets.
Obviously it would be good to make the star, Ryu, of your system, as luminous as possible, in order to make the habitable zone, and the too hot zone inside the habitable zone, as wide as possible to have as many planetary orbits as possible inside each of those zones. There isn't much problem with selecting a star type that might have 12 planets too cold for life beyond the outer edge of its habitable zone.
Possibly Ryu could be as luminous as Rigel, Beta Orionis, which is is about 1.0 to 1.5 times ten to the 5th power as luminous as the Sun. That is about 100,000 times to 150,000 times the luminosity of the Sun. Thus if an Earth like planet was about 316.227 to 387.298 times as far from Rigel as Earth is from the sun, it would receive about the same amount of radiation from Rigel as Earth gets from the Sun.
So how wide, proportionally is the Sun's habitable zone? As I said above, that is controversial and uncertain.
The width of the habitable zone in Astronomical units or AU, has been given as pessimistically as 0.95 AU to 1.01 AU, a ratio of 1.063 times. And as high as 0.95 AU to 2.4 AU, a ratio of 2.526 times. And if the results of different studies are combined, possibly as high a ratio as 0.38 AU to 10 AU, or 26.315 times.
So, assuming that 325.00 AU from Rigel would be the equivalent of 1.00 AU from the Sun, the most pessimistic Rigelian habitable zone would stretch from 308.75 AUs to 328.25 AU, a difference of 19.5 AU. Uranus orbits the Sun at a distance of 19.22 AU, so in our solar system there are 7 planets orbiting the sun within less than 19.5 AU, as well as space for another planet in the asteroid belt.
The most optimistic Rigelian habitable zone would stretch from 308.75 AU to 780 AU, a difference of 471.25 AU. If the orbits of planets in that optimistic habitable zone were spaced 10 AU apart, there could be 47 or 48 planets in the optimistic Rigelian habitable zone. If the orbits of planets in the optimistic Rigelian habitable zone were spaced an average of 1.0 AU apart, there could be 470 planets in that zone.
It is not surprising that Jack Vance, in his famous Demon Princes series, put 26 habitable planets in the habitable zone of Rigel.
With over 300 AUs inside the habitable zone of Rigel, a hundred planets could be spaced an average of 1 AU apart and only occupy a third of the space inside the habitable zone, so finding space for 96 planets too hot to be habitable closer than the habitable zone of Rigel would not be a very big problem.
But you do have two habitable planets in the habitable zone of Ryu. These planets should be at least 3,000,000,000 years old in order to be habitable, and have to had received fairly steady light and heat from their star for all those 3,000,000,000 years. And that is being rather generous, since, it seems like Earth could have been over 4,000,000,000 years old before oxygen in the atmosphere climbed to breathable levels for humans.
Thus the star Ryu should have remained on the main sequence stage of stellar evolution for at least 3,000,000,000 years. Unless the two habitable planets in the Ryu system originated in another star system and remained there for billions of years until super powerful aliens brought them to the Ryu system for some reason. Or unless the two habitable planets originally orbited a different star for billions of years and a very unusual close passage between that star and Ryu caused them to be captured by Ryu.
And the really, really annoying fact about astrophysics for science fiction writers is that more massive and luminous stars use up their nuclear fuel much more quickly and remain on the main sequence for a much shorter time.
The most massive star likely to remain on the main sequence for enough billions of years would be about spectral type F5V, and about 1.5 times as massive as the Sun. Fortunately small increases in stellar mass cause large increases in stellar luminosity.
Astronomers have discovered thousand of exoplanets around distant stars, and sometimes more than one planet in a solar system.
In the CVSO 30 system, CVSO 30b orbits at a distance of 0.0084 AU and CVSO 30c orbits at a distance of 662 AU, a different of 78,998 times, and a difference of 661.9916 AU.
The narrowest difference between the orbits of two planets in the same system is between Kepler-70b and Kepler-70c. Kepler-70c orbits about 0.0016 AU farther out than Kepler-70B. That is about 240,000 kilometers, less than the distance from Earth to the Moon.
Since the pessimistic habitable zone for the solar system is 0.06 AU in width, it could contain 37.5 planetary orbits each separated by 0.0016 AU. If the optimistic habitable zone of the Sun is 0.95 AU to 2.40 AU, it is 1.45 AU wide, and thus could contain 906.25 planetary orbits each separated by 0.0016 AU.
Since the inner edge of the Sun's habitable zone is often considered to be 0.95 AU from the Sun, there could be as many as 593.75 planetary orbits, each separated by 0.0016 AU, inside the inner edge of the habitable zone, and thus where the planets would be too hot.
Another important factor is the relative spacing of the planetary orbits. The smallest ratio between the orbits of two consecutive planets is 11 percent. Kepler-36b and Kepler-36c have semi-major axis of 0.1153 AU and 0.1283 AU, a difference of 0.013 AU and 1.1127493 times the smaller orbit.
Assuming that a planet orbits the Sun at 0.95 AU, a distance often considered to be the inner edge of the Sun's habitable zone, a planet orbiting 1.1127493 times as far would orbit at 1.0571118 AU, (which is already outside the pessimistic habitable zone), a third planet orbiting at 1.1127493 times would orbit at 1.1763004 AU, a fourth at 1.3089274 AU, a fifth at 1.456508 AU, a sixth at 1.6207282 AU, a seventh at 1.8034641 AU, an eighth at 2.0068034 AU, a ninth at 2.233069 AU, a tenth at 2.4848459 AU (which is outside the outer edge of the optimistic habitable zone at 2.4 AU), an eleventh at 2.7650105 AU, and a twelfth at 3.0767634 AU.
So 12 planets each spaced at 1.1127493 time the orbital radius of the previous one would end up with the outermost orbit 3.2386983 times as wide as the innermost orbit. That is too great a ratio for the optimistic habitable zone. But the really, really optimistic habitable zone that could be made by taking the innermost edge from one study and the outermost edge from a different study, would have a ratio of 26.3157, several times enough to contain a ratio of 3.2386983.
It seems impossible to fit a series of 96 planets each with an orbit 1.1127493 times the orbit of the previous one, within 0.95 AU of the sun. A series of 12 such orbits would have a ratio of 3.2386983, a series of 24 such orbits would have a ratio of 10.489166, a series of 48 such orbits would have a ratio of 110.0226, a series of 96 such orbits would have a ratio of 12,104.972. The innermost orbits would be deep within the Sun if the outermost orbit was closer to the Sun than the inner edge of the habitable zone.
So possibly you might want to consider having a ring of 96 planets in a single orbit, orbiting closer to Ryu than the inner edge of the habitable zone, or possibly two such rings with a total of 96 planets.
Note that spacing the planets by the smallest known distance made them fit in well, with plenty of room to spare, even when the star was no more luminous than the Sun, but the 96 planets closer to Ryu than the inner edge of the habitable zone wouldn't fit even if the smallest known orbital ratio was used to space them.
That shows that something that is possible according to one calculation can be impossible according to another calculation.
If the planet orbits are spaced by the smallest known distance between planetary orbits, making the star more luminous will increase the space available and make it possible to fit in more planets.
But if the planets are spaced by the smallest known ratio between planetary orbits, making the star more luminous will not increase the relative width of the habitable zone or the too hot zone, and you will have to make many of the planets double planets, or put a lot of planets in a ring, or find some other highly unusual (but hopefully possible) arrangement, to fit them in.
Before exoplanets were discovered, the smallest ratio between planetary orbits known to astronomers was 1.388888, the ratio between the orbits of Venus and Earth, and the known smallest separation between planetary orbits was 0.28 AU. between Earth and Venus.
The tiny orbital separation between Kepler-70b and Kepler-70c was discovered in 2011, and is one one hundred and seventy fifth the smallest such separation in our solar system. The tiny ratio between the orbits of Kepler-36b and Kepler-36c was discovered in 2012 and is much smaller that the smallest ratio known in the solar system.
Since multiple planets in star systems have only be discovered for a comparatively short time. it is possible and rather probable that planets that are spaced more closely than the current record, both by distance and by ratio of orbits, will be discovered.