Weird; the reason we haven't prioritised it is in that in practice it doesn't seem to be a big problem? You don't get push notifs while you're active in the app itself, and the fact that i get push on my phone while also reading on desktop almost feels like a feature (I often read the msg first via push on phone before then going and hunting on it desktop, especially as Element Web's notification panel needs love).

It's not a problem; it's an intense frustration. It is irritating to be told "here's a new message X" at your desk, only to see and hear the same notification "new message X" on a phone within a few seconds. Your phone even vibrates, as if to demand your attention and chide you for not acknowledging the message. It's an additional distraction when we're all short on time.

My previous work used a system which queued notifications for delivery. The logic was something along those lines:

- send notifications for urgent items, e.g. incoming calls, immediately to all devices - if there are no active devices, send all notifications immediately - otherwise send to all active devices st internally along with testers.

I ended up tweaking this; it took us a few tries to get it right. I'd be flabbergasted if Facebook messenger, iChat, discord et al haven't done something similar.

I can second this, I love being able to answer quickly from my mobile (I type [actually swipe] faster on mobile). It's also amazing how the push notifications clear when read somewhere else, this is not to taken for granted, it's not implemented on most other chat apps and it's a huge advantage of Element imho, sometimes it's buggy¹ but it's easy better than not having it and only Telegram is better in this regard from my experience.

1. https://github.com/vector-im/element-android/issues/4147 and also some other

Maybe you have a different use case for it, than my problem. It seems you are happy when you get a notifications on mobile when web client lost focus. My case is that it notifies me all them time, even if when client is fully in focus and I actively have a conversation.

Often when my phone is left behind somewhere in the apartment, my SO will ask me to do something with those notifications, or just will move my phone away from her (and/or my tablet).

BTW it seems that other communication devices did it right. I just tested Google Chat, and I remember that I did not have this issue neither with Slack.

Is there any other chat app that does this? Or want other app? Would be interested to see a PoC and experience how this feels.

Google Chat as for one example. It feels great ;)