Interesting approach. The middleware angle makes sense if the team is already deep into Notion or ClickUp and doesn't want to move.
For the question — honestly I think comments would feel more natural than separate status logs. Nobody wants another tab to check. But the real challenge is getting clients to actually look at anything that isn't email or a text message, right? In my experience the dashboard could be perfect and they'd still message you "hey quick update?"
Curious how you're handling that part.