App Store: No purchases

Recently set up a new 16" Macbook Pro to replace my old 2016 model. I had a number of apps purchased through the app store, but when I open the app store on the new Mac it says I have no purchases. I've tried logging out/back in, restarting, praying to the old gods, and doing all of the above multiple times while balancing random barnyard animals on my head. Nothing works. It consistently says I have no purchases. I check the App store on my older Mac and there they are, all my purchases showing up. I verified that both are signed into the same account. On the new Mac I open the app store to one of my purchased apps and it says the app is compatible with my device - but prompts me to purchase it rather than install. I don't see any other options for help, support, whatever, just an app store that won't show my purchases.