Unable to install xcode since recent update in my mac m1 pro

I'm currently using Xcode, which is open. I have had various Xcode betas installed, in addition to the Mac App Store version. The latest Xcode RC was simply titled "Xcode.app" and overwrote the version from the Mac App Store in my Applications directory.

As I'm typing this, the "Installing" seems to have finally failed. It has begun downloading the entire 12.39 GB update again.

Why is the Mac App Store download stuck at "Installing"? How can I get this update to actually install?