Maybe it’s a slightly different issue, but still, I’d like to add: I’ve noticed that the task does not ‘auto-resolve’, to put it in your terms, if it involves visiting non-combat nodes, i.e. boons, mysteries or spirit healers, in which case the pop-up thing happens after the next fight on the map.
As for the pop-up delay that you speak of, the game tends to be not be very responsive during that short period, if memory serves, and I can’t confirm or disprove that you indeed can start the next fight at this window of opportunity, but if that were the case, seems like a general lag issue.
No, you could also visit the campfire previously, it just required one more click on the ‘Visit’ (or something like that) button after selecting the campfire icon, which was always there, on the map.
Don’t know and don’t care about Batllegrounds, which are off-topic here, but, speaking of bugs: Mercenaries: frequent crashes on task screen. It’s better nowadays, but still happens occasionally.