I have had the same problem - mail search not working - after installing OS11, Big Sur. But I found a fix!
To be specific, my mail search worked as usual for a day or two after the upgrade, but then stopped working. BTW, my spotlight was working fine, but not finding most mail. Incredibly frustrating, as I search within Mail many times an hour for keywords, names, etc - mostly searching within All Mailboxes. I noticed that mail search was only searching the names of mailboxes, not the content or subject or "to" or "from" of every email. I did check "All Mailboxes", on the left mailbox folder pane (and tried very other folders), but still the Mail search only searched the names of mailboxes....
I have only found this thread with others having the same problem, and I called Apple support (they are to call me back in some hours).
So I figured this out, with help from a YouTube video about the same problem (mail search not working) - but after Catalina install (https://www.youtube.com/watch?v=GCWpJT7NPzc)
The fix: simply, in System Preferences > Internet Accounts > my Gmail account, I de-selected the box checked by Mail, then closed System Preferences to restart and then re-select my Mail in my Gmail account. When I went to close System Preferences after de-selecting Mail, I was led to "security and privacy" window where I was prompted to accept an updrade of sorts. I did not take a screen shot to show... But after that, then restarting and then re-selecting my Mail in my Gmail account, then starting Mail again - it is back to working normal!
I do hope this helps y'all with you fix~
Dave