So I can unpair my watch from my old phone because that phone broke? How do I unpair to connect to my new phone?

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

Unpair and erase your Apple Watch - Apple Support

To unpair and erase watch and remove Activation Lock.

On a computer, go to iCloud.com and sign in with your Apple ID.

Go to Find Iphone.

Select All Devices, then click your Apple Watch.

Click Erase Apple Watch.

Select Next until the device is erased.

Click the remove button next to your Apple Watch.

Then go here;

And now to pair the watch with my new phone.