Nothing in the notification list is stored. Every item is a live read of existing data, so an item disappears by itself once the thing it describes is resolved. That is also why there is no per-item dismiss: there is nothing to dismiss, only something to fix.
Read Is Not The Same As Resolved
Clicking an item marks that one read and drops the badge by one; Mark all read clears the rest. Items stay listed after being read — a campaign you looked at is still waiting for your approval, and hiding it would not make that less true.
Read State Lives In Your Browser
Read state is stored in your browser, so it is per-device and does not sync between machines. Clearing site data resets it, and marking everything read on your laptop leaves your phone's badge untouched.