You can import Outlook mail to TB, and you can transfer mail between accounts in TB, in a limited way, but it might be easier to have your gmail account collect the mail from the account in O365, if that mail is still on the mail server:

https://support.google.com/mail/answer/21289?co=GENIE.Platform%3DDesktop&hl=en

Can you not also add the gmail account to Outlook and transfer the mail from the other account?

It looks like the Outlook email has been archived on the Mac in .olm files. The files are not on the Exchange server. So I need a way to move the .olm files on the Mac to Gmail on the Mac. Can TB do that?

It looks like Outlook on the Mac prevents transferring .olm mail to a Gmail account in Outlook.

I can't help with Outlook details, but if Outlook and TB are installed on the same computer, TB might be able to import the Outlook mail. In TB, Tools/Import..., select Mail, not Import Everything, and see if TB recognizes the Outlook setup.

The basic question is whether TB can import Outlook Mac archived files with an .olm extension (Outlook Mac archive) into a Gmail account that has been installed in TB on the Mac.

The basic question is whether TB can import Outlook Mac archived files with an .olm extension (Outlook Mac archive) into a Gmail account that has been installed in TB on the Mac.

The answer is no, TB can't import any Outlook Mac archive type. Look for software to convert .olm to mbox format, which can be imported to TB.