Sending multimedia content and documents within chat conversations in Microsoft Teams
For anyone following my saga... Microsoft support sent more suggestions. Of the 4, I'd tried 3 already. But then they suggested trying to log in from a different profile (which I happened to have, but never use).
There it was-- the giphy button!!
My IT guys had already dug into my global account, "role' (so permissions) and everything looked fine. But this means it's something about *my* profile. Hopefully I'll be able to update with their solution...and it will help others.