The only issue I see in that log is an apparent failure communicating between the unelevated and the elevated components of the uninstaller. But that doesn't seem to have interfered with the rest of the process, so I'm at a bit of a loss.

Possibly it has gotten confused because of running as administrator to install the py.exe launcher for all users, but not the rest of it.

When you say the system asked for admin right - do you mean you had to authenticate as a different user? Or you had to click "Yes" to give it permissions?