The obvious way to do something like this is to publish a note that references notifications to be cleared by their unique address. It should be "invisible" and not show up on user-facing feeds. It's only effective if multiple clients respect that note though.
Discussion
yea that's what I was thinking. A new note each time you clear a batch of notifications which references the noteIds read. Worst case, you other client doesn't grab the list and the notifications are uncleared on the second client. Best case the noteids included are marked as read. Seems like it would work 🤷♂️