Running the reload command in this other thread works to fix the issue as well:
$ code # BROKEN
cannot create user data directory: /home/COMPANY/myownuser/snap/code/137: Permission denied
$ sudo apparmor_parser -r /etc/apparmor.d/usr.lib.snapd.snap-confine.real
$ code # WORKS
But this is suddenly starting to happen on a large amount of machines, and it would be inconvenient if this command has to be run every time snapd has refreshed.