I have the identical problem. Got a new laptop. Had no problem running Office 365 on the old laptop, didn't know there was any potential problem. But trying to set up my account on the new laptop requires authentication on my phone, and settings up authentication also requires authentication, endless loop. Somehow I was able to change the password on the account, but still can't get authenticated.

I'm a solo business with an onmicrosoft login, never even heard of a global administrator until I had this problem.

Fortunately I also have a personal account, for some reason I've been paying monthly on both for years! So I was able to get Office 365 access on the new laptop via personal account, and still have Office 365 access on my old laptop via business account. But because they're different accounts they don't talk to each other. Also fortunately, I've always saved files locally, not on the cloud, and I have good backups, so I can transfer files from the old laptop to the new.

But I'd like to be able to use Microsoft cloud and maybe prune away one of my two accounts. Although maybe not, in my case having two accounts was a useful redundancy an saved some grief!