It is the notifications icon. This problem of “clearing the list” is one of the reasons the notification system is being re-developed, and as far as I am aware there is no way to re-populate that list. All of the actions that generated the notifications should also show up in your dashboard, but intermingled with all the other stuff that appears there such as taxa and places that you are subscribed to, along with all the new observations from those other iNatters that you are following. It can be a nightmare trying to sift through them all to get the notifications, but can be done if it’s absolutely vital to see them.
for the best place to have discussion:
https://forum.inaturalist.org/t/notifications-on-inaturalist-please-share-your-ideas/374
and these closed topics might give an outline of the sort of things under consideration already:
https://forum.inaturalist.org/t/notify-observer-when-another-user-marks-something-in-the-data-quality-assessment-section/120/17
https://forum.inaturalist.org/t/make-it-easier-to-find-where-i-last-left-off-reviewing-my-dashboard-material/503
https://forum.inaturalist.org/t/how-to-search-for-records-where-youve-been-tagged/6314