> we tend to actually lose agency while angry, but internally I think we actually believe we have dramatically increased agency in the moment
I mean, we do have increased agency, in a certain sense: we are far better at doing (or, at least, motivating ourselves to do, and keeping our executive functioning pointed toward doing without distractions) the things that "we" want to do when angry.
It's just that both the things "we" want when angry (our preferences), and the mechanisms "we" use to achieve those goals, aren't the same preferences and mechanisms we'd use normally. They're a subset, the parts of you that don't require any conscious deliberation to enact. Whatever parts of "you" are entirely implemented by conscious thought, those parts are temporarily excluded from the definition of the agent "you" when "you" are angry.
In the "Elephant and Rider" metaphor for thinking, when the rider steps off the elephant and lets the elephant run, the elephant becomes much better at doing elephant things. It isn't necessarily much better at doing "rider-and-elephant-as-system" things; it's probably worse at those. But if you need a pure-elephant solution to a problem, getting off the elephant can help.
In martial arts, for example, conscious deliberation is never desired. The rider is never as good at micromanaging the elephant's movements as the elephant is at moving itself. "You"—the rider—want to train "yourself"—the elephant—to move this way reflexively; such that, in a real fight, you can let loose the elephant, and the elephant can solve your problem.