I'm in group chats that often devolve into 2-3 talking about something between themselves. While I'm busy with other things I'm not interested in being distracted every single time something is said because I think the notification might be something that requires attention. Once I have some free time I may be interested in going back to see what was said, but if I know they're going off and I don't want to hear about it at the moment I'd like the conversation to automatically mute for a short period of time.

The assumption is that by that point I am aware of the messages and have chosen to ignore them for the time being. There is no need to notify me because I've already been notified

What do you mean, "people like you"?