Server Version#: Synology 1.25.9.5721
Player Version#: 9.0.5.31871 (b0e00ed7) on Samsung Galaxy s10+, but this issue has been present for the ~2 years I’ve been using Plex
The Home screen won’t fully refresh, even when manually pulled down. It will refresh some things on its own / this way, like Continue Watching state, but others (specifically, Recently Added items to TV/Movie libraries) won’t actually refresh unless navigating to another tab (ie another library) and back, OR after some static amount of time (~5-10 minutes? haven’t diligently tracked).
But, the other library Recommended screens have no trouble auto-refreshing themselves fully when squatting on them, so I would expect the Home screen to be capable of the same.
This is a fairly minor annoyance since it is workaround-able, but it is frustrating when adding content to library and not seeing it update, especially after doing a “pull to refresh”, which one would expect to refresh 
