This one is new to me.
If you couldn’t boot from the drive at all, I would ask you to check to make sure your T2 chip is configured to permit booting external drives. But you can boot it (via the option key), so that’s not an issue.
I suspect that it’s a problem with Monterey simply being too new for the Mojave Startup Disk preference panel to recognize. In order to detect bootable volumes, it looks for particular files/directories on the volume. If it doesn’t see what it’s looking for, it will assume the volume to be non-bootable and won’t show it.
In this case, Mojave boots from a single APFS disk volume. I assume its Startup Disk panel will be looking for a single volume containing boot code (boot loader, kernel, other key files, etc.)
Starting with macOS Catalina, however, the OS was split into two different APFS volumes - a System volume (which is a cryptographically sealed snapshot of itself since Big Sur) and a Data volume, which are bound to each other using the APFS Volume Group mechanism. Startup Disk would need to recognize this, look for key files in each of the two volumes, and look for the volume group. Since Mojave doesn’t use this mechanism, it probably doesn’t recognize it, and so won’t show the Monterey system as bootable.
At least that’s my theory at this time.
As for SMART status, macOS does not include the device drivers necessary to check SMART status on USB drives. You need to add third-party software if you want to read it. As far as I know, the only third-party driver to support this is the open source OS-X-SAT-SMART driver.
If you don’t want to manually compile and install it yourself, Binary Fruit ships a signed build of it with their DriveDx product. If you want to download and install their build independently of DriveDx, see their page describing USB support.
Even with the SAT-SMART driver, your USB drive/enclosure will still need to support SMART data - not all do. But without the driver, macOS won’t even try to read it.