How to unpair my Apple Watch from my broken iPhone?

Activation Lock is designed to prevent anyone else from using an Apple Watch if it's ever lost or stolen.

About Activation Lock on your Apple Watch - Apple Support

Activation Lock is an anti-theft feature that cannot be bypassed. Only the previous owner can remove the lock by using their Apple ID & password. Apple will not help you find the previous owner. If the previous owner cannot or will not remove the lock, then the watch is useless to you or anyone else.

If you are the ORIGINAL owner, then see the 'Start a support request' section in:

How to remove Activation Lock - Apple Support

Here are two ways to unpair your watch if you no longer have the paired iPhone:

• See the 'How to erase your Apple Watch if you don't have your iPhone' section of:

Unpair and erase your Apple Watch - Apple Support

• With a web browser, go to: https://www.iCloud.com and sign in with your Apple ID. Open Find My iPhone and select All Devices (at the top). Then click your Apple Watch, select 'Erase Apple Watch', and select Next until the device is erased. Finally click "X" next to remove your Apple Watch.

The simple answer is you are going to need to completely reset the Apple Watch, including remove it from your Apple ID. You are posting here which needs you to login with your Apple ID, so you should in fact already know your login credentials. Follow the steps in

What to do before you sell, give away, or trade in your Apple Watch, or buy one from someone else - Apple Support

Notably,

<quote>

If you already gave away your Apple Watch, you can erase and turn off Activation Lock from iCloud.com. Here's how:

1. On a computer, go to Find My iPhone on iCloud.com and sign in with your Apple ID. 
2. Select All Devices, then click your Apple Watch.
3. Click Erase Apple Watch. Select Next until the device is erased.
4. Click the X button  next to your Apple Watch. 

<end quote>

This should put the watch back to factory-new condition ready tp pair with the replacement phone.