I've tried to narrow things a bit down. With the example file provided earlier, I reduced file size in 50 MB chunks until the playback controls turned up, which was when I reached file size 2085391219 bytes. Then I verified by creating a file 50 MB larger, i.e. 2135391220 bytes. No playback controls there. So I now on this file that just don't works I did
tail -c 50000000 broken.ts > offending_part.ts
and just only played this part. And, lo and behold, I have playback controls, so I'd infer it's not in the data.
I clamied earlier that the problem was not related to file size, since I had 1.4 GB recordings showing the problems - strange enough, I can no longer reproduce it, although I swear they showed the problem! Perhaps at some point the player just gets broken and a reboot is required.
So I picked another, different file not working, and tried shorten it - this time by 10 MB chunks -, with similar but not exactly the same results: 2154473940 bytes have plackback control (larger than above's not-working-file), 2169473940 bytes no longer have playback controls.
Now it comes: After this, the file in the beginning of the post I said is not working, having 2135391220 bytes, is now working - so it is not even a strictly reproducible problem (which might explain why earlier I claimed a 1.4 GB did not work). RAM seems not to be the problem, I used a small python script to eat up loads of RAM, playback control situation stayed the same. Stupid me, ran the script on the wrong machine... will redo... Redid: RAM is not affecting it.
After a reboot, situation remaind as described: only the largest of the truncated files does not show playback controls...
Maybe it is a problem of Raspberry OS still being 32 bit? The above file sizes not working are remarkably close to 1024 * 1024 * 1024 bytes = 2.147.483.648 bytes, and as far as I understand, this is a limit for 32 bit systems. Still, somehow I don't believe that's the reason - many media files are larger... And the second, working is already beyond that limit...
Last thing possible: The Raspberry works through all files in an asynchronous process and stores metadata in its database. And when the files are fresh, the duration is missing. After a while, the process is done and the information is there and suddenly the files work... Still, I don't believe it: Many files not working are there longer than those not working in the beginneng but working now. Still, what I will do is leave the device running for a few hours and see if things have changed...
In the meanwhile: Does what I write above help anyone to get this puzzle solved?
EDIT!!!: Tried something I should have done in the first place: Copied the file from the network location to RPi SD card --> Playback controls are there for the original file! I guess that should help finding th issue...?
Edit 2: Also USB stick works locally, but not via network.