I found a way that resolved the apps unable to update issue on my phone, somehow (not sure quite how) and I wanted to mention it. (I have an iPhone 11 Pro Max and the public beta of 13.3).
I decided to file a bug report for the issue with the Feedback app (that's technically what we're supposed to do as beta testers anyway, right, though I'd gotten lazy lately, admittedly). So, I did that and put my phone aside for awhile. A few hours later, I came back and realized I could update the apps again! I figured what may have happened is that, during the process for submitting a report, the Feedback app "gathers relevant files" from your system to send to Apple with the report and something in that process apparently reset something that allowed updates to work again.
So, long story short, if you can't update your apps, try submitting a bug report about it with the Feedback app. It may help. Note that the process asks you to describe the issue by choosing from various drop down menus, and I'm guessing that's part of it. Don't just submit anything, so it looks for the right files.
edit: or maybe Mothandras was right and it was a server-side issue. (They posted while I was typing.)