The Apple TV app uses a queue list, called ‘Up Next’, for which you can add content manually, and it would also be added automatically when you start watching something in the app. It is not very suitable as a sort of library to collect titles in; it behaves fundamentally different than e.g. Netflix’s My List.
For movies, partially watched movies would stay in Up Next (with a progress bar). Titles watched until the end will be removed automatically.
For TV series (episodic content), partially watched episodes would stay in Up Next (with a progress bar). Episodes watched until the end will be removed automatically, and the next episode (if released) will be added automatically. If all released episodes have been watched, then the title will be removed/hidden from Up Next.
You may make manual edits (remove items one at a time) from the Watch Now screen/tab, then In Up Next.
If needed, all of Up Next will be cleared after doing ‘Clear Play History’ on any of your devices with the Apple TV app.
Apple TV app user guide for smart TVs and third party streaming devices - Apple Support