Angels have the Phone Box
Monk, I'm so sorry - I saw this and completely missed the "stuck in offline" issue!
I have switched several people (including myself) from POP to IMAP, and anyone using Outlook always went from *.pst to *.ost.
I changed my web mail (Gmail) from POP3 to IMAP. Since the upgrade, Outlook creates *.ost data files instead of *.pst data files.
Your switch from a MS account to local login for W10 should have nothing to do with gmail. If your gmail is set for IMAP, Outlook will create an *.ost file. You may, however, still be logged into Office with your MS account, so you might want to check that.
The Outlook "Work Offline" icon in the Send/Receive tab should always have a red-x on it; The globe is grey in color. But, if you are unable to toggle it, perhaps you should try an office repair? You access that from (Control Panel) Programs and Features>Uninstall a Program. When you select Office, you will have an option to Change. When you select Change, you will get an option to repair. Working from memory, there are 2 repair options, one local and one online. If I remember correctly, for the two versions of the repair, one is offline or local, and one is online, which will require you to re-input your keycode and register another activation.
My gmail is IMAP, but I access it through HTTP, not with Outlook. The email I use with Outlook is Charter, (POP), and for some reason, they don't show any options for IMAP in my web settings, so I can't play around with it, to help you....sorry about that.
I hope this helps. Maybe some others will chime in with some additional ideas.