Yeah, it's one of those YMMV moments. If I was in your situation, the easiest way I'd probably do it is to keep stuff separated.Or I'm having ISP problems. We've been over this already I think.
Dunno how many responders we've had in here, but I'm almost willing to bet that no two are skinning this cat in precisely the same way.
Your ripped blu-rays are on the NAS, so keep them there & run the ripped content off the syno video player or get plex/infuse to read them from there.
For Music/TV (newer names for iTunes) purchased content then keep those on the mini (which are downloaded) & can then be seen via the Computers app on Apple TV or Music/TV app on iOS devices using home sharing (to turn on use media sharing options in system preferences). I'm not sure how large your purchased library content is, so again ymmv & your Macmini TV/Music library can be moved if needed.
If money's no option for you & your purchased content library doesn't exceed 2TB, spec the biggest mini you can at the moment (16GB RAM & 2TB SSD) or wait for the rumored Macmini Pro in march which should see RAM & SSD capacities increase & run your purchased content from there using the Music/TV app on the Apple TV.
If money is an option, then get a base M1 mini (smallest drive & I'd opt for 16GB RAM, but if all your using it for is movies then 8GB would probably suffice, there's loads of other threads that discuss this) & move your whole Music/TV (iTunes) library to the NAS which always needs to be connected - there's chat on a syno forum & older instructions which should still work at the end here
When you buy content on the iPad, the mini can automatically be set to download a copy to your purchased Music/TV library folder which is then available to all devices, again via homesharing.
What you cannot do is have a split iTunes library for purchased content where some purchased files are contained within the Music/TV folders on your mac & some other location on the NAS.
My set-up is specific to my circumstances & as I don't download purchases I don't need to move my internal library.
Of course, you'd always see your purchased content in the music/tv apps under purchases, but these would stream.
If I'm wrong in what I've said, others can advise as I use an older macOS, but I'm pretty sure this is correct.