Hello, this bug was ultimately caused by /etc/profile.d/pyenv.sh, which Debian ships.
It sets the PYENV_ROOT to a directory that the user cannot actually write to, in the users environment. This basically breaks all of pyenv for non-root usage; installing versions no longer works even if the shims for shell integration aren't used at all, which is what I'm doing. If there's some need for me to add a bit more urgency to getting the fixed version rolled into trixie, I'd say this is it: pyenv is unusable out of the box for anyone but root even without any shims as soon as the user logs back into their shell, because the profile.d file that is in 2.5.4 but thankfully will be removed in 2.5.5 sets environment variables to something that doesn't make sense.