Your iPhone model determines how much you'll learn. The only way to check if the battery in an iPhone XR, XS, or second-generation iPhone SE has been replaced is to use it. To see if there's been a display swap, you'll need an iPhone 11 or later, and an iPhone 12 or later to see if the camera has been replaced. These warnings will not prevent you from using your device; if you're fine with utilizing unapproved parts and losing warranty coverage, you're fine.
iOS 15.2 is currently available as a developer preview, indicating that the final version will be released soon. It's unclear whether iPad users will see a similar part history function at this time.