OS not starting up, prohibitory symbol

Firstly, you should always have a backup of your files, so there should be no question of losing anything. Files without a backup are waiting to be lost.

If the Recovery partition is indeed on Lion, then it won't read the new APFS formatted disk that Big Sur uses.

Your first port of call should be to whoever wrote the patch, and ask them about whether it alters NVRAM in any way. It's possible that the reset is unrelated, and merely coincidental, of course.

I'd suggest that your best course of action is to get an external drive that you can install some working OS to - even if it's Lion, and then upgrade that to Catalina, which at the least will be able to read the disk. Even a cheap 64GB 'thumb' drive may be sufficient in extremis, (though obviously, you'll be buying an external for backing up anyway...)

You should be able to install Catalina on the internal drive once you're running Catalina on the external.

Contrary to popular opinion, Apple don't cut off hardware from new OSes on a whim -- it's usually because the hardware lacks some specific requirement, or the 'experience' is brick slow.

TBH, there's not much that you'll gain from Big Sur: Catalina will run perfectly well and should be compatible with new apps for a few years yet. But ultimately -- it's nearly a 10 year-old laptop. It may well keep running fine as it is for years, but it won't keep pace with the shiniest anymore.