Good write up @Orko!
I’m seeing the exact same issues.
The separated libraries issue is occurring on iOS & iPadOS clients in addition to the tvOS client for me.
Plex Web shows everything as expected – and in the way I want – by grouping content from multiple movie & TV libraries together into individual movie & TV sections.
I have access to the Plex tvOS app betas, and when the issues first started occurring I assumed they were client-side and I rolled back to a previous version. That didn’t fix it though. So I suspect there’s potentially issues with the clients and PMS.
On the manual ordering issue, an additional problem I have is that when it’s enabled it also breaks the Apple TV / tvOS “Top Shelf” system feature, see this thread.