You didn’t want a psychology answer but it may help to compare two beliefs among emotion researchers. One is anger is a primary emotion and the other is anger is a combination emotion.

I’d propose a third which is that much of what we describe in behavior observations of anger is a combination and very rarely is it pure anger without scorn (disgust) or aggression (with anticipation).

Plutchiks wheel distinguishes combination emotions with primary emotions and puts anger as one of eight primaries. Others speculate that what we are observing as the category anger is actually almost entirely a shit sandwich of fear, disorientation, boredom, approach, avoid, enjoy, not enjoy.

Sometimes it helps to take a step back and realize that it’s hard to even describe anger as pleasurable or not. An approach emotion or a retreat. Advantageous or a liability to a sense of well-being. So that may begin to clue you into the need for more complicated models than a single hormone or chemical.

It sounds like you were looking for more of an ELI5 chemical analysis of hormones in balance such as adrenaline v cortisol oxytocin v dopamine v serotonin testosterone v estrogen.

There’s no topic that’s done less justice by an oversimplified ELI5. Think of all the absolutes that have made us worse for understanding how these function as single chemicals rather than more as combinatorial fractions.

For instance take the commonly held belief that XXY males fill prison halls because of absolute testosterone. That’s not the case. If it was the case the measure would be total testosterone for determining prison wings but it actually matters much more what your testosterone balance is with estrogen.

With anger it may be appropriate not just to think of ratios of the anger related hormones (norepinephrine - dopamine etc.) with the other related chemicals being compared one at a time. Anger compared to the others with each having one on one ratios, but rather three coordinates; X Y and Z. Then using some of those coordinates to be ratios themselves such as the following xyz coordinates -

X cortisol : Y adrenaline : Z testosterone to estrogen.

I don’t have a solid answer for you with even a half way decent or better model than the 101’s. I just have a hunch it will take some measure that is equally or more complicated.

I think Robert Sapolsky took one of the first stabs at making these complexities available to the general public in his book Behave. But good luck if you aren’t deeply really interested in the topic. Behave is no ELI5.