I’ve tested this in creative and survival, using buckets on both naturally spawned fish and axolotls and spawn egg mobs. Neither full nor èmpty buckets work.
I have a video but it won’t upload for some reason.
Edit: I finally found the problem. Everything I read said “tap the fish.” I finally found something that told me to hold down and long press on the fish.
So it was user error.
Resolved on my own. I was tapping the fish, instead of long-pressing on the fish.