Update all devices in the background

**Describe the problem you have/What new integration you would like**
I have 21 devices in esphome that is running in HomeAssistant on a RaspberryPi3, which means that updating all the devices will take a long time.
The problem is that the "Update all" button requires the the webbrowser to remain in contact with the server and the browser that I use (Firefox) will put a webpage to sleep if its not on the foreground, this will result in the update being aborted.
Updating now will require me to keep that browser active, it would be better if the update all action will continue even if the connection with the browser has been lost.

**Please describe your use case for this integration and alternatives you've tried:**
Currently I have the keep the browser active

**Additional context**

Start by tracing the “Update all” browser action and the server-side update handling used by ESPHome in Home Assistant on the Raspberry Pi. Check how the process depends on the browser connection; done means all selected devices continue updating after the browser is closed or backgrounded, with a way to observe completion or failure.

Written by the indexing model from the issue text.