Did you mark it read (by clicking the blue dot, or in some cases by visiting it)?

Alerts are no longer automatically marked as read.

I'm not sure if I clicked on the blue dot, but I did click on some of them, but I don't think this is the issue. I believe there is a confusion on what we each call as "read": I consider normal to have it read (at least for cross-wiki) when the button with the number of notifications turns grey; this means that I have opened the drop-down and I'm at least aware of the existence of the message - no need to make the button red again on each Wiki I visit. You can leave the entry in the drop-down list as unread (white background), even show a number >0 in the button, but it shouldn't turn red on each wiki, especially since it's no longer red on the home wiki.

I think this is equivalent to treating the notification for a particular message as the same in all wikis, not consider each cross-wiki notification a different (new) notification.

I think this ticket is a duplicate of T134855: Make the notification highlights work better across wikis.

In T138569#2461143, @Strainu wrote:

I'm not sure if I clicked on the blue dot, but I did click on some of them, but I don't think this is the issue. I believe there is a confusion on what we each call as "read": I consider normal to have it read (at least for cross-wiki) when the button with the number of notifications turns grey; this means that I have opened the drop-down and I'm at least aware of the existence of the message - no need to make the button red again on each Wiki I visit.

This is "seen" status, not "read" status. It's a complex issue, but we're working on it.