apple watch gps
hi does an apple watch series 5 have to be on the same network as your phone
A GPS only model does not care about your iPhone cellular carrier.
If you are talking about a Cellular model Apple Watch, then the Apple Watch shares the iPhone's phone number, so it absolutely Must use the same carrier, and the carrier will charge the equivalent of $10 U.S. per month to share that phone number.
If you are talking about WiFi, then no, but what a GPS only Apple Watch can do just on WiFi vs with the iPhone nearby are different. The GPS Apple Watch has it most capabilities when the iPhone is nearby
https://support.apple.com/en-us/HT205547
Make sure you read the footnotes, as there is some valuable information in them.