Dear Gideon,
I ran into the same problem yesterday with students accessing a course by means of Safari on Macbooks. On my own Windows laptop I experienced no issues with Edge nor with Chrome but was able to reproduce the issue on an iPad with Safari.
You imply you ran into this issue before so you may already know this: It is not just "Allow cookies" that is needed for OneDrive to connect, it is also "Allow third-party cookies" that needs to be enabled. This setting is named in various ways in various browsers: "Tracking", "Cross-platform tracking" mostly you will find it under Privacy or Security settings.
Hope this helps.
Regards,
Tonnie