Well uranus has an earth sized rocky core so an earth sized planet can handle a gasgiants gas. Venus has a decent amount of gas too while being slightly smaller. And finally the only moon in our solar system with a legit atmosphere is Titian with a methane haze orbiting Saturn. I dont think size is the defining issue but rather the conditions. Rocky planets take longer to form so it’s likely to be not enough gas by the time large rocky bodies form to start collecting gas. Its just unlikely for a planet or moon to collect a large amount of gas without collecting the most in its neighborhood without being destroyed outright, yeeted into deep space, or assimilated into whatever dominant gas giant is in the area. Id imagine the only reason our ice giants have rocky cores is because they formed further out and slower than jupiter and saturn so they had more time to collect rocky material and various ices.

Im not sure if methane would survive without a solid magnetosphere or at that temperature but the only other rocky body with precipitation Titian has an atmosphere of methane.