There’s a ton of research. Though my information is a bit old.

Twenty years ago I did undergrad research at a Notification Systems research group[1] with Dr Scott McCrickard. Much of the research had to do with giving people information in efficient ways that limited attention disruption but also took into account the task (like an emergency to act on vs just information).

As part of this research I surveyed the cognitive psych literature. I remember early research in attention in UX had to do with pilots and cockpit system design. A pilot must take in lots of streams of information while still flying/looking out the window. I also remember that there’s a research topic of “vigilance” - boring tasks that require constant attention. Like being on watch on the bridge of a shop at night or guarding something. I remember people can only stay in this state for 20-25 minutes, and must rotate their job or have a game to play or busy work to do to do this at all well. I also studied “cognitive architectures” which at the time made modeling attention a central focus[2]

1 -https://research.cs.vt.edu/ns/ 2 - https://en.m.wikipedia.org/wiki/Cognitive_architecture