When uninstalling plugins including data the directory is not actually removed and reinstalling the plugin fails unless the directory is manually removed.
The debug log reveals an error when Picard tries to delete the files:
E: 17:01:55,904 picard\plugin3\manager._safe_remove_directory:612: Failed to remove plugin directory for add_to_collection_3713d8f5-72b0-401d-9ec9-3818380bc576 C:\Users\User\AppData\Roaming\MusicBrainz\Picard\plugins3\add_to_collection_3713d8f5-72b0-401d-9ec9-3818380bc576: [WinError 5] Zugriff verweigert: 'C:\\Users\\User\\AppData\\Roaming\\MusicBrainz\\Picard\\plugins3\\add_to_collection_3713d8f5-72b0-401d-9ec9-3818380bc576\\.git\\objects\\pack\\pack-619862f4dfa8562f338dd74074dc7f172221ad1b.idx'