Some MacOS app store functions broken
Sadly, the best solution is to isolate the failure. Take your AppleID to a clean install of macOS (you could download the installer and install on to a USB drive or boot to Internet Recovery and see if you can install on to a USB drive.

Then you'll know if the problem is your computer or your AppleID. Despite the delay in getting to Apple Support - they are the one true source of account information and the best troubleshooting and the inside access to engineering to fix your account and/or get you the best chance of a precise fix.

Sorry it's not some easy thing, but the likely cause is you need to wipe and reinstall your Mac and that might only take a couple hours overnight - especially if you have a backup to restore tomorrow. Ideally you would have a second Mac you could borrow and run the test there if you don't want to touch your main Mac or be sure you can restore your current system to a new OS with no issues brought forward with the migration.