I'm quite sure, however, that my old Blackberry ID had "authority" for the gmail app. If I manage to sign into by old Blackberry ID, would I be able to redownload the gmail app?

Run Windows Store Apps Troubleshooter Update Mail and Calendar app on the Microsoft Windows Store Reset or Uninstall and Reinstall the Mail & Calendar app Enable proxy connection.

If the new Outlook app is not sending or receiving emails on your Windows 11 then you need to reconfigure the account or reset or reinstall the app. Here's how to do it.