Same issues after upgrading to macOS Monterey 12.1. I installed Outlook for Mac beta Version 16.57 (21122200), but the issue is still there. Rebuilding Spotlight database does not help, Outlook still shows "no results" when searching.

Microsoft confirmed this issue: https://support.microsoft.com/en-us/office/search-in-outlook-for-mac-returns-no-results-after-installing-macos-monterey-12-1-075c5f09-35db-4205-aba3-eea2f168c71b

I can confirm that Outlook Version 16.58 (22010406) resolves this issue.