Thank you so much for your answer and suggestion. I will share my experience here as it might help others.
The reason the bot channel service was not responding with the 502 Bad Gateway is because the web app was not running at all, it had silently failed to start.
To see that, in the web app service, click on the URL and if it doesn't say something about web sockets, it's probably not running.
Then, I got some help to realize that in the web app service we can actually browse the logs : the app was not starting because there was a file named <somethingjsonresource>.metaproj and basically the fact there is any file other than the *.csproj ending with pro is enough to block the web app from starting (it says there are multiple project files.... !)
So I re-published after renaming this file and now it all works