I think the likely way out of this eventually is the customizability of the dashboard itself.
We’re in the early days of that story, and you can do some things today like choose which sections to show and in what order, and add reports backed by custom data explorer queries.
I could see the ability to add tiles with other info fitting into the overall design here, and “which version is currently deployed” being an option there.
In the meantime, that “manage updates” page is a good one to build some muscle memory around. It might also get more better in the future too.