A new shared calendar has been set up on our O365. I hooked it up into my Outlook using the 'Connect to Outlook' link within the calendar. While I can see whatever's there and enter/delete things on both ends, it's not syncing between Outlook and cloud... even though mail itself is fine.
I created an appointment in Outlook for next week Tuesday, and in O365 for next week Thursday; neither is showing in the other, even after 10 hours now.
Ticket also opened with MS support; I'll update here with any updates from MS.
Thanks for all wisdom.