Is this the point? To make
summaryseparate for each user and not global (per-app), and keep it up-to-date with the help of a background process that listens to new messages?
Yes, that was my proposal.
One thing that would be a step between here and there but not require a background process would be to just add the JavaScript API to allow updating a local-only summary. Then use summary messages to update the summary as we do now while the app is closed, but when you open the app it can set it to something fully correct when it runs. So it means you always get a correct summary at least right after you open it.