Maybe I'm a bit jaded as I remember the time where windows application didn't even came with a basic uninstaller and didn't relied on InstallShield instead used their own installer.

Also I don't think that there is actually such log, and that "OS level application management" is just the good old "Programs and Features" dialog where it simply registers the path to the uninstaller.

On Linux on the other hand the applications place their stuff in well defined directories and the install script has to deliver the file manifest (and where to copy its content) otherwise the application or library would simply not work. Flatpak kinda does the same but uses a dedicated directory in the users home directory, Snaps uuhm I don't touch canonical stuff with a ten foot pole, AppImage just delete the file and your are golden.