core: Nest Integration - Configuration failed at the very end of the process (once again)

The problem

This issue is the continuation of https://github.com/home-assistant/core/issues/73455 (which was closed since resolved…but not for that much unfortunately).

To resume my problem (which may have changed from the original one), the “add integration” process fails at the very end: when I click on link account, a new browser tab is opened pointing to http://localhost:8123/auth/external/callback?code=***** but remains blank (nothing is loaded nor is loading). If I go back to the home assistant tab a pop-up is present saying something like Loading the next step for Nest. After a while (a minute or so) the message changes to Error.

As suggested in the previous issue, I activated advanced logs with the following lines in my configuration.yaml:

logger: 
  default: info 
  logs:
    homeassistant.helpers.config_entry_oauth2_flow: debug

However, the log is not so verbose:

Logger: aiohttp.server
Source: runner.py:120
First occurred: 18:01:26 (2 occurrences)
Last logged: 18:08:11

Error handling request

I also have this error in the registry but I am not sure it is related:

Logger: frontend.js.latest.202212131
Source: components/system_log/__init__.py:256
First occurred: 17:54:49 (2 occurrences)
Last logged: 18:02:06

:0:0 ResizeObserver loop completed with undelivered notifications.

As fat as I understand, there is no more information on the complete registry (concerning this problem).

In my previous post, @allenporter wrote:

The other related problems here i've seen are my home assistant url is not the same as the url you are using to talk to home assistant

But I did not understand what he meant. There may be part of the solution there…

I also tried to create new credential and then a new Device Access Project to see if I messed-up something, but nothing changed.

Thanks in advance for your help.

What version of Home Assistant Core has the issue?

core-2022.12.8

What was the last working version of Home Assistant Core?

Not known

What type of installation are you running?

Home Assistant Container

Integration causing the issue

Google Nest

Link to integration documentation on our website

https://www.home-assistant.io/integrations/nest/

Diagnostics information

No response

Example YAML snippet

No response

Anything in the logs that might be useful for us?

No response

Additional information

I do not understand why at the end of the process I have home-assistant.io as authorized domain in my OAuth Consent screen; I left it empty in the configuration process as per instructions. By the way, that may be normal…