Hi @Jeff Kilgore ,
Welcome to our forum!
How did you install the Outlook App of M365 without File tab?
As i know, we can install the web version of Outlook—either Outlook on the web or Outlook.com—as a progressive web app in the new Microsoft Edge and Google Chrome, which is the same situation as yours that no File tab is available, as shown in the below figure:
Please check if the Outlook (PWA) is what you are using, if not, please provide a sreenshot of your Outlook App for our better research. (To avoid your privacy leakage, please remember to hide your personal information.)
By the way, considering that you may have some doubts when installing Outlook 365, we recommend that you could try to download Office 365 on this official link: Get Microsoft 365 Apps. You can check which Office you have installed successfully via Control Panel > Programs and Features:
In addition, for your original question, we can also add account in Outlook via Control Panel > Mail > Email Account:
Hope the above help!
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