Not possible. The Apple watch cannot be set up with a plan that is different to the one on the iPhone.
Your carrier will set up the watch so it shares the same number and plan from the iPhone.
https://www.imore.com/how-cellular-data-works-apple-watch#carrier
The Apple Watch will then take on the same number as the iPhone so calls to your iPhone arrive at your watch.
Unlike Apple's a-la-carte iPad plans, a GPS + Cellular Apple Watch is intrinsically tied to its parent iPhone plan; this allows you to receive phone calls from the same number even if you're out and about. This means that you:
- Have to have a phone plan that currently supports eSIM (the technology used to connect the watch's cellular service)
- Need a phone plan that currently supports adding the Apple Watch
- Can't sign up for a different carrier on your watch than on your iPhone
In practice, this is pretty simple: When you set up cellular data on your Apple Watch, you'll be redirected to your current iPhone carrier's portal for Apple Watch, where you can add on a ~$10/month plan based on your carrier and region. There's no option for picking your own carrier like the Apple SIM, so you can't hack your way around your provider offering support for another LTE watch but not Apple's own.