If I get one notification, the red badge on the app icon often shows "2". This usually happens when the notification is a chat and may happen for other notifications as well. Now that I've reported it I will try to keep a closer eye on what the situations are, if that helps.

I can confirm I've seen this as well.

A related request: would it be better if the notifications showed how many conversations had unread messages in them instead of how many unread messages there are? I woke up to 35 notifications the other morning and it was just a conversation in the public chat. If they just showed conversations with new messages then it would have just been 1 in the red dot.

Sub spottings, new specialist hires available, and other players' specialist hires all increase the badge number by one.

We'll definitely fix the double notifications (and flaky notifications in general) sometime soon.

As for the number in the badge, we're trying to match people's expectations on this. Most people will be used to iMessages/WhatsApp or other messaging apps, and I believe all increase the badge count per message and not per thread, right?

Increasing the badge count the same as the number of unread messages is fine.

If I have two unread chats, one from each of two players, there will only be one extra number added to the badge.

The ingame badge on the chat icon is accurate even if the iOS icon badge is not.

yup, there's a rewrite of the whole badge system on our list, we just haven't gotten around to it yet. it will all be consistent once it's done.