To summarize:
Searching messages in Outlook for Mac 16.52 or above does not work. In fact, it hasn't worked properly since 16.42, but now it doesn't work at all.
Earlier releases of Outlook for Mac do not work in Monterey, the OS currently shipping with Macintosh computers.
Mac computers cannot be downgraded to earlier OSs.
Outlook for Mac has an option to enable "New Outlook." Doing this will, among other things, result in search working properly (or so I've heard).
New Outlook does not work with on-premise hosted email. It only works if the Exchange server is O365.
Therefore, the only way to search for content in Outlook for Mac is either not to buy new Macintosh computers, or to agree to pay Microsoft for use of their "cloud" Exchange server to host mail messages, then go through the process of migrating all our users to it.
For many of us, that simply cannot happen for legal, operational, and/or technical reasons.
I really hope somebody in the catacombs of Microsoft understands the gravity of the situtation.
Jeff