We are indebted to GanawaGangunawa for figuring out why Mail search was failing on Emily's M1 MacBook Air (known to our family as "Crashy" ). It's a Big Sur bug (though I think it happened in some Catalina environments) that hits multi-user machines.
In our case Ben and Emily both have non-admin accounts on her M1 Air running Big Sur 11.2.1 with fast user switching enabled. When Ben logs out Emily's Mail search stops working. There's no error message, but search does nothing and Smart Folders are inactive.
The fix is to kill corespotlightd.
I created an AppleScript with the contents:
do shell script "killall -9 corespotlightd"
I saved it as an application and put it on Emily's dock. Two clicks fixes her Mail search until Apple fixes the bug.
 When we first got the M1 Air it crashed (spontaneous restart) every few hours. Reinstalling Big Sur meant it crashed every few days, with Big Sur 11.2 it didn't crash, with 11.2.1 it restarts every week or so. I suspect a firmware/OS mismatch in the factory was the initial problem and that for the rest that Big Sur/M1 are not quite stable yet. I almost returned Crashy in the 2 week return window but it seems just stable enough. Good chance future OS updates will fix. It does pass hardware test.