MacBook Diagnostics Not Working
I attempted to run Diagnostics, but it did not work and I found I had lost the “.diagnostics” folder when I wiped the hard drive.

When you reinstall, Apple Diagnostics will get reinstalled as well.  If it’s missing, it calls into question how you did said reinstall.  Booting from Recovery, wiping the drive and installing macOS will leave a pristine, fully functional version of macOS on your drive.  If you’re missing things, this was an “out of band” re-install (meaning non-standard).  When that happens, you’ll have the devil’s own time trying to pinpoint the cause of your troubles.

I followed the instructions in this post (Replacing &quot;apple hardware test&quot; with &quot;apple diagnostics&quot;) but the problem

No!  Don’t do this!  First off, Apple has diagnostic procedures specific to their machines.  You can’t “willy-nilly” change them because you feel one is better than the other.  Even when you upgrade, Apple doesn’t change your diagnostics.  For example, a Mid 2012 MacBook Pro which is capable of running Catalina still uses AHT.  Catalina doesn’t upgrade it to Apple Diagnostics.
How do we know this?
Apple tells us in their support document How to use Apple Diagnostics on your Mac:


If your Mac was introduced before June 2013, it uses Apple Hardware Test instead.


Secondly, it’s well known that Apple’s diagnostics lose usability with each subsequent version, so “upgrading” to a later version will actually give you less useful diagnostic data.
Use Internet Diagnostics
Your Mac has the ability to boot from Internet Recovery; it should also have the ability to boot Internet Diagnostics.  Boot your computer while holding OptionD (obviously you need an Internet connection). This will ensure that you download and use the correct diagnostic utility for your Mac.
Do a clean, proper install of macOS
Based on what you described, it sounds like your install is a bit of a bodge.  My advice is to clean things up so you’re  working on a solid footing.

Back up your data. Verify that it’s good
Wipe your drive clean
Install the latest version of macOS (Mojave if you need 32-bit app support; Catalina if not necessary)
Make sure Recovery (hold CommandR) and Diagnostics(hold D) works
Here, step 5, is where we’re going to figure out what’s causing your crashes.
Once you have a stable system, use Migration Assistant to move your data over.
Verify that everything is working as it should.  If so, immediately make a backup and verify.