‘Up Next’ is supposed to show a row of content tiles of shows and movies that you have partially watched, and shows of which you have not seen all available episodes (if you watch in order), and manually added content of which you may not have seen any part. [It is intended as a queue list, which may act a bit differently than watchlists in other apps.]
All the way down on the Home tab, the last row on the page, you would additionally find a row of Recently Watched movies and episodes (completed).
In the Apple TV+ tab of the Apple TV app, you would find a secondary Up Next row, specialized for Apple TV+ movies and TV shows (not mentioning content from the Store or other in-app channels).
Up Next, Recently Watched, etc., may not reflect your watch progress if you have chosen to turn off Use Play History in Settings for this app. Verify that it is set to ‘On’.
Apple TV app user guide for smart TVs and third party streaming devices - Apple Support