mail search doesn't show mailbox

And if you are using Column Layout, you can choose exactly what columns to appear.

Control-click on the header and check or uncheck as needed:

Hey there David,

Let's team up to get Mail search working as expected. To start, we'd like to confirm the following details to better understand what's happening, along with ruling out some possible causes:

1. You mentioned that a specific mailbox doesn't show in your Mail search results, but do other things show, such as other mailboxes?
2. We see you have macOS Monterey, but the latest version is macOS Monterey 12.6.1. The latest version available is macOS Ventura 13.0, but it's not necessary to upgrade at this time. We still recommend making sure macOS 12.6.1 is installed. You can verify this by clicking on the Apple logo at the top left corner of the screen, then on ‘About This Mac’. This link will show how to first back up, then Update macOS on Mac.
3. Sometimes unexpected behavior can be resolved with a restart. Check out the section 'Restart' here: Log out, sleep, wake, restart, or shut down your Mac

Cheers!

I don't use Column Layout myself, but this way of selecting columns has been something common on the Mac for a long time.

It also works exactly the same in Finder (in List View), for example. As a long time Mac user, it feels natural.

This capability was removed from Mail a few years ago (though it always worked in the Finder), and I remember lots of people complaining about that.

Oh, and not only you can choose what columns to see, you can also order the columns - just by dragging the headers, and you can sort by column, just by clicking the header. All pretty standard features that at one point (Mojave or Catalina) failed to work, and were brought back in Big Sur.

Are you using "Column Layout"?

I do not use it, and I still see the mailbox in the search results.