macos – OS not starting up, prohibitory symbol

I have a Mid-2012 MacBook Pro with Bootcamp, and it supports only up to MacOS Catalina, and not Big Sur. This frustrated me and I decided to go off the rules a bit & installed MacOS Big Sur (using patched Sur). This was all working fine, until a few days ago, I reseted the PRAM as I was having some issues with the CD-ROM.

The problem started here. After I reseted the PRAM, the MacBook started showing the prohibitory symbol. It scared me a lot since it had a lot of data (class notes, reference books for exams, etc.), and for the past 3 days, I’ve been searching the internet for its fix.
So, by now I’ve come to know that this sign comes when the Hard-Drive contains a MacOS, but it’s not supported on the Mac. Obviously, it contained Big Sur, which was not supported by this model.

On doing Internet recovery, it gave an option of reinstalling MacOS Snow Leopard, but when selecting a disk to reinstall the OS, it shows only the Bootcamp partition of the Hard Drive and shows the message that it’s locked.

So, I wanted to ask if there is any method of reinstalling MacOS (and obviously this time I’m not going back to Big Sur, only upto Catalina. This experience was enough) without losing any of my data, both from bootcamp and MacOS? If not, then is there a way I could back up files of MacOS partition from Bootcamp partition?
Also, is there a simpler way to bypass this check, like the bypass created by Patched Sur, as that’ll mean I’ll not have to go back to Snow Leopard and reinstall OS updates to go back to catalina?

Also, I wanted to know what exactly happened when I reseted the PRAM, that this bypass stopped working? This needn’t include in the answers, but info on how this happened will help in expanding my knowledge.