I've been using university-licensed Office for a decade across several fresh MacOS Installs. Only in the last year have I started frequently receiving "sign-in to verify license" nags not unlike the OP's. These also cripple editing functionality until you sign in, forcing you to do the 2FA dance every time. The same rot afflicts mobile apps lately. It's such bad taste to perform license checks this aggressively.

Teams is also flaky on the Mac. About 1 in 4 times I join a call Teams gets stuck and I either must restart it or use the browser (which never fails). This has recurred across multiple physical Macs.