I can't restore macOS Catalina 10.15.7 despite Shift-Option-command-R combinations on startup

According to How to reinstall macOS - Apple Support —

• Command-R start offers to reinstall if you have a current version with a working recovery partition, otherwise it may try to download from Apple which requires a working network / WiFi connection
• Command-Option-R offers to reinstall the latest compatible version (Catalina)
• Shift-Option-Command-R offers the closest version to the original (possibly Mountain Lion if that's even possible to obtain any more)

Try these and report the results.

Failing that, you may be forced to create a bootable installer disk using another machine, but this is a useful thing to keep around afterwards and I think you only need a 16GB USB stick for the bootable installer disk. Download a fresh copy from Apple to make sure that the app signing is up to date.

Besides the USB Bootable option Mike Smart recommends, might try tis...

Error 2002u… Router needs DNS setting...

I was getting pretty frustrated at this point, but I finally found a post on the Apple Support forums by someone who was having a similar problem to mine (different error code, -2002U if I’m remembering correctly). With only one reply, I didn’t have my hopes up for a way out of this mess. Nevertheless, I looked it over.

The sole solution suggested going into my router settings, changing my DNS to 8.8.8.8 and/or 8.8.4.4 (Google’s public DNS server addresses,) and trying again.

https://medium.com/@lucchetto/2018-1-d4b628a2587e