I cannot open or play song's with anything but Files (default file explorer on AndroidOne I have a new Nokia 3.1. After putting in and formatting an SD card, I copied a tonne of music to it (in Music/ in the root folder). This is m4a and mp3 files.
Every music player app I get (Musicolet, Pulsar etc.) will not find the music automatically; will not find it when forced to rescan; will not play it when it is sent to the app via Files.

'Files' and 'Google Play' will see and play the files. Musicolet (the only one out of 10 different apps) will scan the files, pick up that they're all there - and then not update the music library or show anything.

What the hell is going on? It seems only default apps can see and play music - although not very effectively, since I don't want to pay or use internet to listen to my own collection

I've tried clearing temporary storage, uninstalling/reinstalling music player apps, restarting the phone - same story.

Please please god help, if I can't play music I may as well not own this phone. The Nokia 3310 can play music fgs.
Android uses a media database ("Android MediaStore Database") which is used by most apps. If the file has not been indexed by the database or is unknown to the database it doesn't exists for the apps.

If you have copied a "tonne of music" this database may be a bit overloaded by indexing all the uploaded music files (or may be even crashed). 

Therefore I would first wait a while and then re-check if the media files are now visible in the player apps. If after some hours the files are still not visible, reboot the device. This usually triggers a re-scan of the media files.

Furthermore the actions I presented at the end of this answer also can be applied in your case.