On what device is this happening?
Do you seek assistance, or did you feel the need to share an opinion?
Slow.
The UI responsiveness will differ by device capability and connectivity.
Navigation.
Navigation is based on presenting series and movies in a way to help discover new content while browsing, using defined TV design themes. Not monolithic rigid grids. Which may be progressively different from how others do it, and possibly different from what you were used to.
Search topology.
Please elaborate.
Lack of a user library.
You must be referring to the Apple TV+ app, or website, which indeed has no library, unlike the full Apple TV app on select other devices. The Apple TV+ app has no library, as a single subscriptions service has access to all subscription content all the time, as long as you subscribe. There is an Up Next row to administrate in-progress content that you watch/follow. Apple uses a library for purchased content (buy, rent), not subscription content.
Get the Apple TV app or Apple TV+ app on your smart TV, streaming device, or game console - Apple Support