Plex no longer sees my Hauppauge WinTV-quadHD tuner, "Add Device" scans forever

Thanks for the new logs

You are running two instances of Plex Media Server.exe in parallel - one as a service or scheduled task and the other as a normal user logged in process - the default for auto start on login

Anything can happen when you do that and results indeterminate and there will file locks / corruptions

If you run as a service, you must disable the auto start on login

Better still, use a tool that already exists PMS As a Service and is used by many users (including myself) - see PMS as a service - General / Tips, Tricks & How-Tos - Plex Forum

and if you have multiple user accounts in windows - then look at the update to the registry here PMS as a service - #4 by sa2000 which ensures the Plex Media Server.exe is not autostarted in the windows account used for the PMS install