How to boot into recovery mode on Catalina?
I would get a backup and not worry about the recovery partition until you have time for an erase install or some processes that can take an hour (or more if you don’t have the Catalina installer up to date and downloaded).
Your disk layout is generally good - no issues that are easy to diagnose and fix. In the mean time make sure all your data / backups are current. When you’re ready, you will want to get an external drive and erase the drive completely (not just erasing a volume, but complete erase per this page)

https://support.apple.com/en-us/HT208496

Many people will select Macintosh HD and erase it, rather than erasing the container, so be sure you follow the “How to erase your disk” part and not “How to erase a volume on your disk” portion.
Then run the installer to install on the blank drive - once that is done, you can hold the option key to test things boot, migrate data in from backup and make the call if and when you do the erase on the internal drive.

If you wanted to try a half measure, delete any old installers you have (including stand alone bootable installers) and get a copy of Catalina fresh from the App Store and run that installer one time. It might fix the built in recovery partition, but I really don’t like messing with things at this point. Yes, we could fix your one issue - but it shouldn’t have broken and what else might be broken as well that you don’t know about. Better to erase IMO.