Game Center entitlement is not added to Xcode when using “ProjectCapabilityManager.AddGameCenter”

How to reproduce:
1. Build the user’s attached “AddGameCenterBug.zip” project for iOS platform
2. Open the “AddGameCenterBug.entitlements” file
3. Observe the file

Expected result: “com.apple.developer.game-center” is in the file
Actual result: “com.apple.developer.game-center” is not in the file

Reproducible with: 2021.3.29f1, 2022.3.6f1, 2023.1.6f1, 2023.2.0b3

Reproduced on: macOS 13.4.1 (Intel)

Note: not reproducible with “projectCapabilityManager.AddSignInWithApple”