Scan not removing old link files

A scan and empty trash should remove unavailable files. The scan will identify them as unavailable, and emptying the trash removes the entries from your server. Not sure why that is not happening.

The TV library is pointing at E:\TV Series P1\, correct? Not at the root level, E:\, a show folder, E:\TV Series P1\See (2019), etc.

A Plex Dance will definitely clear things. However, you will lose played/unplayed status, etc. It erases all information about the show from your system. It is like you are adding it to your server for the first time.