Push notifications on mobile

As a user, i do not want to get push notifications on my mobile phone when actively chatting with another user in the desktop client.

With the window open, in focus, and cursor in the input box: I still receive push notifications on my phone each time the person on the other end of the conversation sends a message. After that conversation, i had about 200 notifications to clear on my phone. To clarify, i would still like to receive push notifications if i am not active on the chat if this is possible.

No files, tests, or entry points are named in the issue. Start by tracing how desktop chat activity and mobile push notifications are coordinated; done means notifications are suppressed while the desktop chat is focused but remain available when the user is inactive.

Written by the indexing model from the issue text.