Given that you can get to 95% of the install, I'm going on the assumption that you don't have a firmware password nor FileVault enabled.
First thing I would do is go a step further with the erasure of the disk. More than likely, you've got APFS containers set up and if one of the volumes is corrupt and you're not properly removing it (via the format), this boot loop could be a symptom. So, let's wipe it clean and put a plain macOS file system on it (not APFS). When you boot into Recovery, launch Terminal and type the following command:
$ diskutil JHFS+ "Macintosh HD" disk0
Normally on a MacBook laptop, the internal drive is disk0, but to be completely certain, you can do a diskutil list and look for the "internal" drive, similar to what's below:
/dev/disk0 (internal, physical):
Next, once you've done that, reboot your Mac, again into Recovery. You likely don't have to reboot, but let's start nice and clean. As for operating systems, you should be able to install Catalina, but if you run into issues, try installing Mojave.
When you go to erase the disk this time using the GUI version of Disk Utility, erase it again, but this time use APFS format so it can create the necessary volumes in the container. Then proceed with the install.
This should "get you back to back to zero" - a phrase that means back to where you started. When you go to install Big Sur, get an external USB 3 drive. It doesn't have to be large - 64GB should be fine, but I recommend USB 3 for the speed. Don't install Big Sur (or any beta OS for that matter) on your "work machine." If things go sideways, like they did here, you'll have trouble getting back. By installing and booting from a USB drive, you can easily revert back to your original macOS.
Best Answer
I would get A external hard drlve and install the software on that, then use target fish mode to transfer files. Then erase Mac and install macOS. Then you would transfer files over.