The watchlist and search/discover results used to display the library name, but no longer displays this information.
The primary issue is that media grouped into libraries based on type (4k, foreign, alternative versions) are no longer easy to identify. For movies, it simply says the quality (but does not indicate if content is Dolby Vision, etc), and TV shows only list number of seasons, so it’s not possible to tell if a show is 1080p or 4k.
Please re-add the library name to search and watchlist results.