Sorry, but this is wrong.
I am on EE in the UK. The below is not carrier dependent or country dependent. If i turn off my phone and pullout the SIM for good measure
I can do the below:
Make and receive calls to/from ANYONE on any device - all they need is a phone number.
Receive/send Mail on the watch
Receive iMessages (not SMS)
Stream music
Stream Podcasts
The eSIM will relay all calls to your watch regardless of what make of device is calling.
There is a lot of confusion on this thread and scaremongering - I have had and use a cellular AW for a year now and I have no issues when my iPhone is off/flat.