The animals are not spawning at the surfaces of Dripstone caves and Lush caves. but other mobs except animals are spawning normally.
And also, Minecraft wiki says, Dripstone caves is indistinguishable to normal plains biome, but among the structures that are naturally created, NPC villages and Pillager Outpost aren't created naturally.
I saw the the similar issue with this has been fixed from 21w03a update, however, It seems to have been fixed just for hostile mobs. so, I think this issue is not really duplicate with
There are some screenshots about lush caves and dripstone caves, and a few more screenshots were taken from the Plains biome to compare to the plains and dripstone caves.
I checked the doMobSpawning gamerule hasn't off, and also checked the biome id is 'minecraft:dripstone_caves' and 'minecraft:lush_caves'.