First of all, the Solus update notification in Discover now appears.
However, it will only appear once, whereas in Solus Software, the notification will appear every time you log in, until you process it.
This means you'll have to click the notification as soon as it appears in Discover to process the update of packages and thus, avoid forgetting it (or make a note of it to process it later).
But it's still a real plus.
13 Solus updates to process in Discover this week, and only the "Inspector" package was processed.
Discover refused to process the other system update packages, requesting to do it again later (unfortunately, I didn't note the technical details of this anomaly).

I tried to process these system updates in Solus Software, and everything went well.