Nether cave lava seems to be hardcoded at 32, the default sea level, and cannot be changed in any way.
If the depth of the world is decreased, it is still always 32 blocks above the bottom.
Edit: Added a reference pic. The one to the right is the sea level, and you can see on the left it stays hardcoded at 32 above ymin
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I have done both. Changing the sea level affects most of the lava around the dimension, but then it doesn't fill up to that level in the caves. There is something in the nether cave carver called
"lava_level":
{ "above_bottom": 80 }
Should this not fill up to ymin+80? that is not the case. It seems to be hardcoded at 32 and ignores this value

Yep, it definitely ignores it. Added a reference pic. The one to the right is the sea level, and you can see on the left it stays hardcoded at 32 above ymin

Does this issue still occur in 1.19.4?

Still an issue in 1.20.4.
Have you tried just changing the sea level in the noise settings? Modifying the nether_cave configured carver?