Unable to receive emails when my Apple Watch Ultra 2 is on cellular connection

• Cellular connection appears to be working (signal bars visible)

that is hardly enough verification that it works, and if it do not then that would be the explanation to your issue

try doing other things which would rely on internet access when the phone is away from the watch, like imessage and other watch stuff that use the internet.

if those things works then maybe the carrier you use on the watch do not allow access to the port that the mail account rely on to receive mails.

if it's the isp which do not allow activity on the ports then you can troubleshoot with them with the info that

gmail rely on port 587 or 465 

and exchange rely on various ports

Exchange account port - Google-

i've had issues with carriers which by default pretty much only allowed port 80 (this is the webbrowser port)

Reinstalling the mail account may help, check this external discussion page:

Help with Exchange and Gmail on Cellular only - MacRumors Forums