Is it necessary for me to be paying for number share on Verizon with an Apple Watch Ultra 2 ?

If you want to use your Apple Watch Ultra 2 without your iPhone nearby and not connected to Wi-Fi, you will need a cellular connection.

Use your Apple Watch without your iPhone nearby - Apple Support

In most cases, the carrier plan for the Apple Watch has to be from the same carrier as your iPhone, and will share the phone number of the iPhone.

Did you already check the Verizon Support page about that?

Number Share Overview Verizon

Number Share FAQ's Verizon

That’s the way that carriers do it. When I added my Apple Watch Ultra, it shares the number for messages and calls, for data it has a separate data plan from the iPhone.

Ultra uses an eSIM so you really have no choice.