Internally, for assigns we keep it simple.
Usually to signal something is done, we simply unassign and reply with a comment indicating it’s done (sometimes with a bit more detail about what we did). If it was just a post within a topic, that’s it. If the whole topic represents the todo, we also close it.
When things get more complicated than assign → done, and/or involve multiple people working together, what we reach for is the Kanban theme component.
That is how we can have status decoupled from assignments, with multiple topics sitting in “up next” or “in progress” assigned or unassigned.
That said, the Kanban component comes with its own limitations and idiosyncrasies. We make it work, but it’s something we’re considering revisiting in a more serious way in the near future.
I’d love to learn more about what kind of work you are managing together when we get a bit further along in deciding what we’re doing there.
I haven’t personally used the status feature built into assign yet myself, but perhaps that’ll meet your needs here sufficiently if you get your immediate question answered – have you tried looking at the list of assignments on your user profile?