(Un)fortunately there was nothing for me to solve, it was a bug on Squarespace's end. The email I got from the support team confirmed as much. The good news is it looks like they've sorted it out!
I had to put up a new page for our New Year's Eve menu today and tried throwing in a little html/markdown just as a test and it rendered correctly.
@mattgyver I don't know if you got a response between the 16th and now, but it would be worth checking your page to see if your menu formatting is now displaying correctly! I dropped a screenshot in from a chunk of my breakfast menu - font color, text weight/style, line breaks, and links are all working as they should đź‘Ť