I suspect that no Uninstaller/Cleaner application will find any LinkedIn software to remove because no such app is likely to exist, unless it has been downloaded/installed by a User. The Icon that generally appears in Installed Apps when Windows 11 is first installed is simply a shortcut/link file and in my experience there are two options for removal, which have always worked for me as a permanent solution (providing no prior attempt has been made to use the LinkedIn 'shortcut'):
1) Right-click on the Icon and choose Uninstall - The icon should simply disappear.
2) Right-click on the Icon and select 'Show in finder' - You should see the offending LinkedIn icon/shortcut file (and possibly a few others you might not want/need). Delete the icon and reboot the system. - It should be gone from the Installed Apps settings page.
The only other thing that it may be worthwhile checking is that there are no references to LinkedIn in the Windows Startup settings.
My understanding is that this irritating behaviour (for all non-LinkedIn users) is not Microsoft actually installing PUPs, but providing a 'helper feature', which is able to assist with the auto-integration of the 'service' with various Microsoft Apps, e.g. Outlook. Why Microsoft deems it necessary to cater to the needs of a minority of Windows users in this way is anyone's guess!