AppleTV keeps trying to play purchased TV shows with Paramount+ instead of my Library

Try removing the show from the Up Next queue list (click-and-hold, then choose Remove). Then resume from your library. That would add the show back to Up Next, this time with hopefully the correct working link to the preferred content provider.

I’m having the same issue with a couple of other tv series that I have purchased. It’s very annoying. Always asking if I want to watch on paramount +, despite having purchased the show on Apple TV

I've been experiencing this for at least a year, primarily with Everybody Loves Raymond the complete series as well as The West Wing the complete series.

Everybody Loves Raymond wants to open in Paramount+, even with the app deleted and trying Urquhart1244's suggestion of removing it from the queue list and resuming it from the library. I don't subscribe to Paramount+ so I'm forced to see which episode I'm on in "Next Playing" and then go to that either in my Library or in TV Shows and select the next episode to play. Neither one will keep track of that last played if I leave the respective App.

The same thing for The West Wing, only with MAX/HBO Max for where it's pulling the next episode from. I do have a subscription for MAX, so it's not as much of an issue, but it's still the same issue with this "Complete Series"

Of note, I have other "Complete Series" shows from Warner Bros/MAX that don't behave this way