Once a product is published, you watch it from the Server console rather than from the pane you built it in.
Start at the Overview
The Overview answers the first questions: what's live, how much of your plan you're using, and whether anything has drifted — meaning Production is running behind a newer release you haven't promoted.
Drift isn't a fault. It's a decision waiting: read the newer release's note, then promote it or hold off on purpose.
Look at one API
The APIs view lists your published APIs and what each environment is currently serving. Filter it by environment when you only care about one.
You can disable a deployment to stop it serving without losing anything — re-enable it and it's back on the same URLs.
Read the logs
Each published product shows its recent request activity. That's where you answer the practical questions: is anyone actually calling this, are the requests succeeding, and does the problem someone reported show up on our side.
Look back with Activity
The Activity view records every release, promotion, and rollback, with who did it and when, and exports to CSV. When you need to work out what a consumer was getting on a particular date, start here.