I imagine you could address this in Slack by just having everyone set themselves to 'Away' by default.
One of the things that I've found useful in Slack is turning off the "Someone is typing" message (the option is in the Display Options). I used to wait for someone to post if I knew a message was coming. Now I can drop in and out of a channel more easily. Similarly, I've muted almost all the channels I'm in so now I only need to check if someone notifies me.
The point I'm making is that Slack doesn't necessarily work the way you want right away, and that you might need address a few cultural problems with the way your team uses it. You need to think about how your team communicates, consider why people do annoying things in it, and come up with solutions that work. At the most extreme that might be writing a competitor product but for most companies there just needs to be a little more tolerance of people not answering immediately and a little consideration that gifs can be unhelpful.