Switching providers - confused about how to also switch my cellular Apple Watch

I have a cellular Apple Watch SE and an iPhone 12 mini. I live in the UK and currently have a SIM only plan with EE for my phone and I am paying an additional £5/month for cellular connectivity for my Apple Watch. I can’t remember now whether or not I was given an actual physical SIM card for the Apple Watch or not. I know as far as EE is concerned it comes up on my bill as another phone number / line, but when someone tries to call my phone number it comes through to my watch as well.

I want to switch to Talkmobile, but when I phone them up to ask about how to switch my Apple Watch over, they seem clueless. (I am expecting to have to pay a fee per month for the data it uses.) I have read somewhere that Apple Watches do not need a physical SIM card because they have an eSIM inside them. How do I get my Apple Watch to switch from EE to Talkmobile? Talkmobile don’t seem to be able to tell me how it will work. (I have spoken to two different customer advisors). I was expecting them to say I’d need to pay for an additional line or something. It was as if they don’t know anything about it.

Can anyone shed any light on whether it is possible to get cellular Apple Watch working with Talkmobile, and if so what the procedure is for switching over to them? Any advice would be much appreciated , thank you.