Bug: git-subtree: splitting subtree fails when subtree was added, removed and added again

I discovered a problem in git-subtree that I could also reproduce in a 
minimal proof of concept over at
https://github.com/tionis/git-subtree-bug-poc

The same bug was discussed some time ago on stackoverflow: 
https://stackoverflow.com/questions/68761778/git-subtree-cache-exists

It seems to occur when a subtree was added, removed, alter added again 
and then modified in some commit.

This leads to some error with the cache leading to an error message like

fatal: cache for $commit-hash-here already exists!

I'm unsure how to work around this other than modify the history or 
creating a branch from before the first addition and fixing it there.