BTW: you can look at the cells with the WordList function and see if those are what's holding things up. If your x in 13.x is > .01 and there is an issue there you may want to test the WordList function separately and, if it is not working as one expects, report that as a bug. Let me know and, if that is the case I will download a prerelease and test over here and if there's an issue I will let the developers know.

I sent a copy of the notebook to your mass.edu email address that I have and here is what I wrote in the email (BTW, I would not be the one to kill you for your x>0.1 but I don't have a prerelease installed at the moment):

*Hi Murray, I am attaching my copy of the MWordle.nb notebook. When I execute the whole notebook, the places where it takes a little time to complete are those that included gathering various words using the WordList function. On my computer these (there are two functions with WordList) each take 10 or 15 seconds to complete (of course I could get those words, Iconize them, and include them in the notebook but that’d make is a larger notebook). When the notebook has completed executing I then execute MWordle[Deploy] and the mini application opens up. (Note that you have to click in the individual squares to type in them — you can tab between them — I did not figure out how to automatically type and have the characters go into these input fields. That’s a project for my retirement! Best regards, David*

Works fine for me on "13.0.1 for Mac OS X ARM (64-bit) (January 28, 2022)". Perhaps try with a fresh kernel?