Hi there Patrick,
Upon pulling up Game Center on our own iPhone, we didn't see anything like what you're describing, but we'd like to help however we can.
The first thing we noticed from your post is that you're running iOS 14. The latest for your model is iOS 15.1. You can verify this within Settings > General > About. Here's a link that'll show how to first back up, then Update your iPhone, iPad, or iPod touch.
Once you confirm you've backed up your iPhone and are up to date, we did find a little blue section titled 'See how your data is managed...' at the bottom of Settings > Game Center. It has more details regarding what you're asking.
We were also able to find a website with a more general overview to Understand and control the personal information that you store with Apple.
Take care!