Push events only when all devices are not active

I am using element for Mac or Windows and next to me there is a mobile device. A normal use case in my opinion. All devices are using the same account. When chatting with someone via the desktop client the phone gets a push notification (ntfy server and client) on each message that I receive. This is very annoying. Is there already a feature to get this behavior under control?

No files, tests, or entry points are named. Start by locating Synapse’s push-notification handling and how activity across devices is represented; determine the expected behavior for simultaneous desktop and mobile sessions, then verify it with focused coverage. Done means messages do not push to inactive devices when another session is active, while still notifying when all devices are inactive.

Written by the indexing model from the issue text.