Are you sure about that, or might it be office bullshit? I did a bit of searching around since that sounded a bit strange to me (why would my unpaid personal mail be allowed but not a business account?) and I can’t find a single mention of this. I did find several articles describing the setup process and prerequisites, including official ones from both Google and Mozilla, which don’t mention any such thing:
Google Support
Mozilla Support
Independently written tutorial specifically aimed at Workspace
If I were you I’d just try to follow the steps and see what happens. IIRC it was a royal pain to get oauth to work since my organization requires 2FA, but that’s supposedly been fixed in the latest version.