Photoshop Elements o Monterey system?

Adobe's System Requirements say nothing about Monterey. You will notice a pattern in the annual releases or updates to Photoshop Elements in that they raise the bar for the OS by one year also. The current version seems to be 2021 (not unreasonable in January 2022!) and it supports only macOS 10.14, 10.15 or macOS 11 (at least officially).

Have you found that Elements does not launch in Monterey, or that there are functionality problems in Monterey?

I don't know who you mean with "they", but when you upgrade your OS, you may find older software no longer working. Before an OS is released, Apple makes it available to developers so they can update their software. They may decide to make it compatible with the new OS, may charge for the update, or decide they will not update it. That is up to the developer; technology changes so fast - you cannot expect older apps to work indefinitely. That would only work if you never buy a newer computer or never updated your OS.

So, check with Adobe to see if they plan to update it or not. Also check with the scanner mfr if it is compatible.

Photoshop Elements 2022 works fine on both Intel and M1 Macs running Monterey 12.1 and later.

Had some difficulties but managed to get PSE 22 downloaded and working on Mac Monterrey. I can only access Editor through Organizer and it seems slow, but it seems to be working.