Sync in game center doesn't work

Hi, I can't sync a game between my iPad and iPhone. The email on my profile (game center) is exactly the same. I'm playing on my iPad, and that's fine. I have an iPad Air and an iPhone 13 Pro.

Then, when I go to the game center on my iPhone. I see the game icon in "activity". If I click on it, it goes to the APP to download. I download and the game starts as a new game (beginning), not at the same stage/level that is on my iPad.

I've updated both iPad and iPhone to the last version, the iCloud drive is not full and the game center is using the iCloud.

I would love to get any help to get the game sync between my devices.

Thank you