I got the information from the Microsoft support that they are aware of this issue and working with Apple on it.
More information will be published on this website:
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
"STATUS: INVESTIGATING" - I hope they will find a solution soon.