I have an iPhone 13 and use an e-sim for personal and the sim tray for work mobile. Cameras work fine on wifi but they seem to struggle to decide which data to use even when I set the mobile data to one particular sim. I have had to go back to carrying 2 phones but when separated, they work on the cell data no problem!
Thanks for posting here in the Community. To confirm, what is the iOS version of your iPhone? Have you tried to check if there are any settings that you need to change with your e-sim? Have you called Apply and ask them about the settings of your e-sim? Particularly about cellular data usage. Let us know how it goes.
I am experiencing the same issue on my dual sim iPhone SE 3 (v16.4.1, but also back since I got the Nest camera for Christmas 2022). Once I disable my secondary sim card, the live feed inside Google Home app works just fine on cellular data. Weird that it's behaving this way!