SeitzM appreciate the response - so I tried this out and added my main MSA that is attached to my M365 subscription as the "primary" account, but still no good. I think this is the issue for me since my primary account is through Gmail:
If you purchased a Microsoft 365 Personal or Family subscription with a Microsoft Account that was created with a non-Microsoft email address, you will need to add an Outlook.com alias in order to connect it to Outlook.
Going to try this and will report back to see if it works!
[Edit] Didn't work - I created an Outlook.com alias and tried to add that into the new Outlook client but it said it doesn't recognize the e-mail. What's odd, however, is I reset the Outlook app and went into the desktop client of Outlook and hit the "try new Outlook" toggle, and it brought in all my exchange accounts (that do not have licensing for apps tied to them) into the app without issues. Not sure if that's a bug or what. But now I'm able to add my MSA accounts, lol.