Apple Watch Cellular
Do you have to pay for a plan with your mobile data company for your applewatch?
Apple Watch Series 8
That depends.
If you buy a cellular Apple Watch, and you want it to be able to make and receives calls and messages when away from the paired iPhone, then normally you add a watch fee to your iPhone's plan to get service on the Apple Watch.
If you get a GPS only Apple Watch, or don't activate the cellular portion of a GPS+Cellular Apple Watch, then you don't need to pay anything extra on your iPhone plan.