V16+ schema requires new implementation of sync badge

[mikehardy]

on v16 after full sync, review, undo, sync, the sync badge is still active 🤔 ? also it appeared on full sync that the media check / sync did not run - or at least it was different then when I did a sync after the full sync - on the sync it did an extra dialog with media check stuff

I want to temporarily sunset the sync badge. It's based off DB access which won't work with the new backend and I don't deem it to be higher priority than getting this in. I'd rather we removed the display logic and added a cleanup to recode it in a manner which works with the new backend

Originally posted by @david-allison in #11740 (comment)