There is a suggestion for this on the feedback site:

https://feedback.minecraft.net/hc/en-us/community/posts/360048099592-Wither-skeletons-drop-charcoal-instead-

I think it’s so coal can be renewable in the nether and you can’t make blocks of charcoal.

It may also be related to the stone sword. When mining stone in the overworld, you will likely encounter coal ore, so there may be a correlation there. Possibly finding coal when they found the stone to make the sword.

No. For what reason? It doesn’t make sense for withers to drop nether stars or for cows to drop steak when burned to death by a fire aspect sword. The game is much better this way.

Am i getting gaslighted? They do drop it on bedrock.

im pretty sure they do