Phew, finally.
So I ended git bisecting at this point:
km²~/downloads/:git/emacs> git stash save && git bisect good
Saved working directory and index state WIP on (no branch): 1f55925 ; Fix breakage from previous commit
HEAD is now at 1f55925 ; Fix breakage from previous commit
Bisecting: 0 revisions left to test after this (roughly 1 step)
[0644e6f56d2be82dd716478eb65e7b3c761d813d] Fix copying properties in 'format' when it produces padding
Building emacs using that commit shows that bug.
I don't understand what the C code does. But the comments make somewhat sense as that code change has to do with the format function, and thus related to the incorrect text properties of eldoc hints.