Why is my Apple Watch Series 7 serial number invalid on the Check Coverage website?

Is your serial number and watch listed in your account information?

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1. Go to mysupport.apple.com.
2. Sign in to your Apple Account.
3. Choose your device. 
4. Click View Proof of Coverage. If you don't see your proof of coverage, make sure that you set up your Apple Account with two-factor authentication.

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copied from: Find information about your warranty or AppleCare plan - Apple Support

You should contact the official Apple Support and ask them to look into your personal data, to find out, if your Apple Watch is still tied to your Apple Account.

Contact Apple for support and service - Apple Support

If you open the WatchApp on your iPhone, Got to My Watch/General/About -> Serial Number, do you see the same serial number as when you bought it new?

On that screen you should also see, that your One-Year Warranty has been expired.

Did you buy your watch directly from an Authorised Apple Reseller or Apple?

Has it been replaced by Apple in the past?

Did you use the same Apple Account to pair your watch to your iPhone?

I can see all my Apple devices that I still own on that page, even if bought years ago.