Hi Conor, today I have installed release 13.1.
It seems that the PacletDocumentationBuild is working now, and my Mathematica is no longer crashing.
Not sure if anything has changed, but at least it works, which is great!
However, I do get some errors while running, although they don't seem to influence the build.
For the documentation, I get this error, the referred file is indeed there but cannot be deleted I guess.

When I build the HTML I get the same but when the build starts with the symbol pages these errors pop up for each page, which is not the case for the guide pages.

And again there are some issues with the reference.nb file.

When installing the Paclet I often get this error. If it happens its always the same file that gives the issue and I have to quit the kernel to recover Mathematica, after that it always works immediately.

Happy to see everything working!