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.
The short answer, is do not install Big Sur on 2013 / 2014 MacBook Pro if you can wait. Stick with Catalina if you can and need it to be stable and supported.
Thank you for this post - I found myself in this exact situation, following the same "Apple recommended" procedure to perform a factory reset after already updating to Big Sur. I was left with a useless (likely needing repair) machine until I found this post and followed the steps to reinstall OSX and then upgrade to Catalina.
Second, I found this post here: https://mrmacintosh.com/big-sur-11-0-1-20b50-released-to-block-install-for-2013-14-13-mbpros/
I believe that we had previously upgraded to Big Sur 11.0.1 20b29, released November 12th. However, Apple released an "updated" version, 20b50, on November 19th that removed the late 2013 and mid 2014 Macbook Pros from the compatible list, due to issues that left some users with blank screens.
I imagine that once Apple fixes these blank screen issues, we'll be able to upgrade again.
Also see, "Release History" in https://en.wikipedia.org/wiki/MacOS_Big_Sur
Best Answer
I ran into a similar issue when trying to create a bootable installer for Big Sur as well. I found this page to be helpful:
https://mrmacintosh.com/big-sur-installation-failed-an-error-occurred-while-installing-the-selected-updates/
Basically you open Safari and access this URL to directly download the installer:
http://swcdn.apple.com/content/downloads/50/49/001-79699-A_93OMDU5KFG/dkjnjkq9eax1n2wpf8rik5agns2z43ikqu/InstallAssistant.pkg
For me, it would pause every minute or so, but I just kept clicking resume and eventually I had downloaded the whole thing, and I was able to generate a working bootable installer that has worked on at least 2 macs for me.