I mean, on the same level of seriousness as most Disney films. Think 101 Dalmatians which is a bunch of puppies trying not to be skinned alive. Or Shrek which has torture, family separation/imprisonment (one of whom is later skinned and turned into a rug), floating eyeballs, a tyrannical monarchy etc.
And just like Star Wars, it would feel a little odd to put a gritty/serious movie in either of those universes without a dramatic retooling a la Cruella, which even then wasn’t wildly serious. In my opinion at least.
(Also, I don’t think we see any genocide in New Hope. Are you thinking the Jawas? Because that struck me as standard killing, not a “kill all Jawas.”)