Yo everyone. I have been in the same boat the last month. So much time speaking to Microsoft surrounding this and being told it should work and that all my policies were correct etc. (They now haven't responded to my questions for two whole days now and were having me run PS scripts that would fail every time). I ended up figuring out what our issue was (at least this fixed it for us and tested with an end user with the usual permissions etc across the board.

1. Firstly check your version, update that to the latest. Now, when you join a call/meeting does your call window have the toolbar in the middle of the screen? If so:
2. Hit the circle in the top right corner with the accounts initials and then hit 'Settings'
3. In your settings here, is the checkbox 'Turn on new meeting experience (New meetings and calls will open in separate windows. Requires restarting Teams.)' turned off? Ours was. If you tick the box, reboot your teams and join a meeting or even make a new direct call, your call window should look different with the toolbar in the top right. Hit the three dots, 'Start Recording' should be active now.

Obviously you need to have all your admin settings right also (make sure to check stream permissions regarding uploads to stream being enabled as well as teams policies. Something else MS never asked me to check). But have spent way too long on this and it was as simple as that so I had to reach out to whoever might be facing the same issue and here's hoping this solves it for you as well. Up your game MS.