See if you can find the book “Habitable Planets For Man” by (IIRC) Stephen Dole, publ. Rand Corp. Probably long out of print, but in you local good big library?
He goes through the criteria that would make a planet habitable. FWIW:
Oxygen is 21% at 14psi; or about 2.8psi partial pressure. generally, anything up 8,000 to10,000 feet is “livable”. So that would be about 3/4 sea level? 1/2 bar is at 18,000 feet. Oxygen for pilots is required, IIRC, at 12,500ft?
Odds are that a planet with less than about 0.6G has lost too much atmosphere over a geological time. As pointed out above, hydrogen and oxygen do not last long as separate gasses. H2 boils away first if free. Odds are about 1.4G is the limit of what we would tolerate as a livable heavy planet.
Nitrogen narcosis is a problem. Not sure what the limit is, but IIRC 200 feet for any length of time is a dive limit; 33 feet per bar, so that’s 6 atm. I have this theory that oxygen partial pressure in any atmosphere is pretty self-limiting; if it weren’t for plants constantly refereshing it, ours would all combine with something - carbon, calcium, iron - and disappear. Too high an oxygen concentration and even the wet jungle would burn. Just for fun get an chem major to demonstrate - safely - what happens when you light a match near pure oxygen at 1 bar. Sci Fi authors compensate by saying Argon or some other inert gas is a significant portion of their fictional thick atmosphere. (It’s what, 1% or so of ours?)
As mentioned, there’s a habitable zone that fits just right around certain classes of stars. the stars are classes OBAFGKM(Q) ("Oh Be A Fine Girl Kiss Me Quick) in order of size, heat, and age. The bigger OBA stars are thought too young for an earth-like planet to evolve. Smaller K and M stars may be too small. Dole posits that if the planet is too close, it locks like the moon to face its sun; one theory says, scifi aside, that configuration cannot be habitable. A large moon (or the “planet” is a moon) or a binary planet may be habitable closer in and so get full sunshine. Regardless, since most stars are KM and small, maybe 10% of stars could harbour habitable planets.
then there’s awhole mss of other factors; a planet like Jupiter is surrounded by such a strong magnetic field that the radiation is to intense for a habitable planet inside that zone. A planet needs the big internal magnetic field (Mars lacks) to generate the protection against solar and cosmic radiation. etc.
Always fun to speculate…
Our sun is a G, Alpha Centauri A and B are F and K, IIRC - conveniently close and about right. Epsilon Eriandii IIRC is a G star at 10 light years…