Upgrade from Mojave to Catalina - Recovery mode doesn't show option to convert to APFS filesystem

Hi everyone,

I'm currently trying to upgrade my 13'' Mid 2012 MacBook Pro from macOS Mojave to macOS Catalina. This is not possible due to my SSD, which I built into the MacBook by myself last year, not being converted to the APFS file system but is still in Mac OS Extended (Journaled) instead. I tried to convert it by booting into recovery mode by pressing cmd+R during the boot process and then using disk utitlity to change the file system of my SSD.

Unfortunately, the Internet Recovery mode gets activated upon pressing cmd+R (which seems a bit odd to me) and loads a very outdated looking recovery mode and utilities (e.g. it gives me the option to reinstall MAC OS X). The disk utility program does not have the option to convert the SSD to APFS file system, I guess it's because the whole recovery mode that was loaded up is outdated. So, my question is, how can I get into a "current" recovery mode that gives me the option to convert my SSD file system to APFS? My guess is that my recovery partition might be deleted or corrupted which is why I can only use Internet recovery mode which offers me outdated utilities. But I have no idea how I could fix this.

I have a time machine backup on an external HDD.

What I tried so far:

Reset PRAM by pressing cmd+option+P+R while booting to restore a possibly corrupt recovery partition. Did not change anything.

Thank you for your help!