Apple Watch
If I want the security of a cellular watch that can call 911, do I pay a monthly fee to my cell phone carrier?
Apple Watch Series 8
If you want to do that without carrying your iPhone then yes you need to have your iPhone and your watch set up with a carrier that supports eSIM on iPhone and Watch, and yes there is certainly an additional fee. In USA I believe it is around $10 a month.
If you are happy to carry your iPhone or have it within Bluetooth range there is no need for a cellular Watch to dial 911.
To see which network providers in your country or region offer cellular service for Apple Watch, refer to the chart below.
Apple Watch - Carriers - Apple
You need to buy your Watch in your country of residence and use.