Restarting Xcode and simulator did the trick: now my in-app purchases load properly in iOS 13 simulator.
EDIT: This happens in release Xcode 11 too. And happens once in a while, but restarting Xcode and simulators still helps.
EDIT 2: In Xcode 12 beta this bug is also present. But the solution is to create new StoreKit Configuration file (in File -> New
menu)
Then add all your products there. Use the same product id’s as in AppStore Connect.
Then add this file to Run Scheme configuration.