Thanks, Julien! As usual your suggestions are quite good. Having thought about this for a while, I think you could go far towards addressing your need simply by setting norms within your organization. E.g. clearly communicate with everyone that topics in certain categories will be assigned to specific people who promise to respond within a certain number of days. That way people will hopefully be patient and wait for your response, and you will know which posts to respond to first. In the odd case where you need more time, you can add a reply to let people know when you will reply and maybe explain why it will take some more time to research or whatever hte reason. And then set yourself a reminder.
Did you know you can assign specific posts in a topic to a group or to a user? You can assign it to yourself or a support team, and thereby communicate with everyone involved that the post has been seen, and a response is coming. Assignments then appear on the groups page.
I do think that it’s coming to be time to start talking about adding more task management features to Discourse which I think will also help your use case. This means the ability to set deadlines or target dates for assigments, and potentially even dependencies. E.g. user B can start work on assigned post 2 once user A has finished assigned post 1. Also calendar and kanban card view of assignments for more easily organizing tasks and prioritizing them.
We do have Kanban Board Theme Component but I have not used it in a while. Would be interesting to see if that could be added to Discourse for Teams.