Sounds like the recovery partition is from Mavericks and very old. Best thing to do is backup your data using Time Machine or a clone tool such as Carbon Copy Cloner or SuperDuper to an external drive. Then create a bootable macOS installer for Catalina on an
8GB+ 12GB+ flash drive (prior to Catalina 8GB+ was sufficient). Boot from that and delete everything off the internal drive of the Mac. Then install Catalina and restore using /Applications/Utilities/Migration Assistant and point it to the backup drive.
In the past there were utilities and techniques to remove the recovery partition and recreate it. But it's far cleaner and better to just backup everything then nuke and pave so to speak with a clean install. Those utilities exist but you won't get the latest recovery partition and the only time I used such a method was when I needed to recover a very old system that wasn't upgradable to the latest macOS.
I would not restore from backup at the start of the installer as it might put things back to the way they were (restoring your Mavericks recovery partition) and you would be back at square one. The Migration Assistant should restore your Apps and data once you have a clean install of macOS and updates. Then update your full backup to a new Time Machine backup drive or re-clone it at this point to ensure your backups have the new recovery partition.
You could also hold Option + CMD + R while powering on to use Internet Recovery to upgrade to the latest macOS that is compatible with your Mac and nuke the internal drive completely. But this requires unfiltered WiFi and a fast connection or it will take forever. Burning a flash drive is faster even with the best WiFi / Internet speeds.