We are at my org, but my only exposure is cross-team / cross-division chatter. I collaborate with my team across offices through an old Jabber client. This isn't ideal, but pulling it away from a browser window allows you to disconnect, set DND status, that sort of thing.
Zulip's focus on streams & discussion topics (over people-groups) is terrifically handy for tuning into large-scale group chatter, looking at things that are interesting to you and sharing conversations with others. Project/task management via Slack or any similar tools just seems bonkers to me.
We tried Zulip for a week but the team decided to not continue the experiment. I personally really liked the UI and the keyboard-centric workflow, but the lack of polished UI and the suboptimal mobile experience was really difficult to defend.
Another problem is that we would often end up replying to the wrong thread because of the way the general view is organized.
We are now trying Twist (https://twistapp.com) and it is a very good compromise between the efficiency of Zulip and the polished UI of Slack. The main advantage over Zulip is that you only see one complete thread at a time in the main column, but you can see the last message of each thread you've subscribed to in your inbox (second column): when you hit reply, you are certain that you are replying to the right thread.