I had a similar issue (though unlike others who posted on this topic, I was able to search in Notes). When I searched in Mail, after upgrading to Monterey, I got no results.
I found a solution that worked for me, and it is in this post:
https://www.macobserver.com/tips/how-to/fixing-broken-mail-search-macos/
I went through the first set of steps, which did not fix it. Then I did the second set (deleting the Mail.app indices - just as the instructions state) though mine were in V9 (for Monterey I suppose) and rebooted. My 78K messages took 11 minutes to load back in, and after a few minutes, Search appears to be working now and I hope this helps you or others.