Microsoft AutoUpdate logs to /Library/Logs/Microsoft/autoupdate.log on macOS.
Paths are printed exactly as Microsoft AutoUpdate writes them. Environment variables like %LOCALAPPDATA% and $XDG_STATE_HOME are never expanded, so a path can be pasted straight into a shell. Where a path differs between installer types or shipping flavours, each one is racked as its own card below - why that happens.
Update log/Library/Logs/Microsoft/autoupdate.log- INFO level by default; `defaults write com.microsoft.autoupdate2 ExtendedLogging -bool true` for debug.