GREAT ! it now works for me.
Didn't work since I bought a Mac Pro 14" M1 / Monterey, updated to 12.1, and transfered my old data.
Even with reindexing Spotlight... (Outlook was 16.56).
Works now with Outlook 16.57, coming from "Preview" Channel. So, the culprit was not Spotlight or Mac, but Outlook.
No need to reboot. Just close/reopen Outlook, and the search bar works !
Thanks for all of you !