I can’t pair my existing watch with a new iPhone even after resetting my watch

Make sure your ios is updated to 15.2, then Try a hard reset on your iphone

Force restart an iPhone with Face ID

To force restart iPhone X, iPhone XS, iPhone XR, iPhone 11, iPhone 12, or iPhone 13, do the following:

Press and quickly release the volume up button, press and quickly release the volume down button, then press and hold the side button. When the Apple logo appears, release the button.

If this doesn't work, sign put of icloud, restart your phone and sign back in. Then try again.

From a web browser,sign in to iCloud.com with your Apple ID.

Go to Find iPhone.

Click All Devices at the top of the screen.

Click your Apple Watch.

Click Erase [device]. Select Next until the device is erased.

Click Remove from Account.

Then go here;

How to pair your Apple Watch with a new iPhone