Does Apple Watch 3 pair with iPhone 13?

For Apple Watch to pair with an iPhone you need

• To use your Apple Watch Series 3 or later with watchOS 8, you need to pair your Apple Watch with an iPhone 6s or later with iOS 15 or later. Setup assistants on your iPhone and Apple Watch work together to help you pair and set up your Apple Watch.
• To use your Apple Watch Series 3 or later with watchOS 7, you need to pair your Apple Watch with an iPhone 6s or later with iOS 14 or later. Setup assistants on your iPhone and Apple Watch work together to help you pair and set up your Apple Watch.
• To use your Apple Watch Series 1 or later with watchOS 6.2, you need to pair your Apple Watch with an iPhone 6s or later with iOS 13 or later. Setup assistants on your iPhone and Apple Watch work together to help you pair and set up your Apple Watch.
• To use your Apple Watch Series 1 or later with watchOS 5, you need to pair it with an iPhone 5s or later with iOS 12 or later—Apple Watch models with cellular require an iPhone 6 or later. Setup assistants on your iPhone and Apple Watch work together to help you pair and set up your Apple Watch.

The apple watch 3 GPS only has only 8GB of internal storage, most of that is taken

up by the operating system and other critical software with not much space left for the

update.So installing or even pairing to an ios15 phone is proving nearly

impossible for just about all the watch 3 users on this forum.

same applies to Apple watch 1 and 2 they are almost impossible to either pair or

update with an ios 14 or ios15 phone.

Your best course of action is to call in at an apple store and ask them to pair/update it for you.