Same issue on Mac Book Pro 14 on Monterey. Outlook shows no search results. Tried following steps:
Deleting/Adding exchange account
Installing Outlook again
Adding and removing Outlook Profile from Spotlight privacy tab per https://docs.microsoft.com/en-us/outlook/troubleshoot/outlook-for-mac/useful-tools
pepperwhite
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Updating Monterey from Version 12.0 to 12.0.1 fixed this issue. Outlook search now working as expected.