Apple didn’t share your Apple ID. What’s happening is that apps can store data in the Keychain. Usually this would be login credentials, but they can also store other data, such as a token or some other identifier, that will allow the behaviour you’re seeing. Deleting an app doesn’t delete Keychain data. If you turn on iCloud Keychain then this data will be synced through iCloud.

On iOS, you can only see app and website passwords in the Keychain. On a Mac, you can see all data in the Keychain using the Keychain Access app. Just checked mine, and as an example, there are things like com.instagram.users.persistent_accounts and com.google.sso.GeneratedDeviceIdentifier (although it doesn’t look like you can see the actual data inside these). Things like that are what allow apps to retain info.