One time I had issue with getting mail notification on my watch, I have to go to the watch app on iphone > Mail > Accounts and login to my email accounts. Some of them shows "Sign in required" for some reason. After that the mail notification works perfectly on my watch.
Not sure if it's the same as your issue though.
When there is a notification, I can use my apple watch to separate out notifications that I need to immediately respond (e.g. important message/call from work or family) vs ones I can take care of later without taking out my phone. Before having the apple watch, I have to take out my phone every time when there is a notification.
I also use Apple pay with the watch all the time without taking out my phone.
Both of these use cases works with non-cellular version as well. Of course you'll need your phone nearby or have wifi so you can receive messages, but it doesn't require you to have a cellular watch or have the cellular plan on the watch.