In a multi-pane tabbed interface like cmux (I made my own), I found it sufficient for agents to always alert when they are done or awaiting my input, and then the tab shows a badge that counts the number of unacked alert panes inside it.

Then I just work through the alerts and handle them as they arrive.

I guess there's an edge case where you don't know if an agent is running in a tab at all (while herdr will show "Agent running") but in practice I'm the one starting agents, and they run until they alert, so I'm not hitting a case where I think an agent is running but it's not.