The settings wireframe on that page includes text that @oSoMoN has added in Focal: “Snap package updates are checked routinely and installed automatically.”
Ideally, I think, that text would be dynamic to summarise your current settings (for example, “Snap package updates are checked Mondays and Fridays.” or “Snap package updates are checked five times a week.”). And it would be followed by a “Details…” button, which would open a secondary dialog for controlling the schedule as well as listing recent updates.
Sometimes I design things in the hope that someone will implement them someday. I haven’t had time to do that with this dialog.
But if anyone here is interested, a simple first step — useful and releasable by itself — would be to add a caption below the new label, of the form “Last check: Yesterday 16:27”. If someone submits a merge proposal to do that, then I’ll design the next bit.