Downgrading from Monterey to Mojave, and recovering data from Time Machine

You never want to use configuration files from a newer app/OS on an older app/OS. Unless you are 100% certain the configuration file layout is unchanged & identical....avoid it since if the newer version has changed something, then it will break the old app/OS.

Anything with libraries or databases such as iTunes/Music, iPhoto/Photos, Mail, etc. will have changed over various OS versions so the newer versions of those libraries/databases cannot be used on an older OS.

You will need to manually transfer the data files. I don't know if you can access them through the TM app. If not, then you can manually copy them temporarily to another drive and transfer them back once you have performed a clean install of macOS Mojave. Just make sure you don't miss or forget anything since once you erase the SSD, the data is gone for good except for what you transferred or what is in your backup.

Keep in mind Apple is only thinking about moving forward, so Apple never considered that anyone would want or need to move backwards.

Unless you have a TM backup from when you were using Mojave then you will have issues using the backup from Monterey. I did this only one time and found many of the app files (especially Apple ones) from the newer OS had issues with the previous older OS. You can try and see what happens.