I have a number of connected Nest devices, and when I open the nest app it takes 10-15 seconds of a spinning nest logo before I can see any of the devices on my home screen.
This is annoying for managing all the devices, but really problematic for a video doorbell, as when anyone rings it will be at least 15 seconds before I can respond to them even if I have my phone in my hand!
This latency can also be observed at home.nest.com on the webapp, so it isn't really iOS specific. I'm sure it would also happen on the Android app.
Yeah, I'm trying to use the Google Home app more and more as well since the Nest app/products are being deprecated. I just wish the Google Home App had more functionality like scheduling, and I hope they release the web version sooner than later. But, you are correct, Wifi does play a role in connection. After installing 6 Nest cameras, I broke down and had to replace my Wifi router, and it made all the difference in viewing live video. They pop up instantly now.