How do I delete recent purchases in my Apple TV library

You can hide them so they don’t show: Hide and unhide music, movies, TV shows, audiobooks, and books - Apple Support

If you mean the category itself, rather than individual movie titles:

The Recent Purchases category orders your purchases by purchase date: last purchase first mentioned. Take ‘recent’ with a grain of salt, as it can have entries from many years ago if you buy just a few top titles. I suppose this list is maximized by total number, but I haven’t reached that limit yet. You can’t hide the category as a whole.

I think it maxes out at 8. When I add a new one, the last 8th one moves off the list