My 6yo is like this and has just been diagnosed with ADHD. It's the emotional regulation which he is lacking, so any time something should provoke a slightly annoyed reaction it's basically like it shoots him up to enraged and then he can't wind it back. It's the same for all emotions. If he's excited he's too excited and it's annoying. If he's sad it's the end of the world and he is in floods of tears.
My eldest was similar but he didn't get diagnosed until he was older. He is 16 now and so chilled he is basically horizontal 
I had absolutely no input on how to manage him when he was little, so we did lots and lots and LOTS of talking about feelings - but outside the moment, when he was calmer. Not in the moment as he couldn't take it in. At that time I just used to put a door between us, which didn't feel like the most appropriate parenting ever but I had no idea what else to do! He did grow out of it. He also didn't have a sibling. Now I have a 3yo as well like you, so I felt we needed a different response. Also, the assessment got pushed through because DS2 doesn't mask at school. Whereas DS1 did.
IME neither a stern, punitive response nor a calm "Oh you are feeling angry!" response will help. The first will escalate things in the moment but not reduce the behaviour over time, sometimes it will also increase stress generally or actively be confusing/feel unfair to him because he genuinely wouldn't understand why he had got into trouble - and the second is just noise to them and doesn't do anything to resolve things. But it did seem to be useful to talk about feelings outside of the moment (which is also what we have been advised to do for DS2).
The most useful things I've come across have been:
The book Big, Baffling Behaviours - this explains how the nervous system can go into "defence mode" and also sort of identifies several different levels of their nervous system being riled up, so you can pick your approach based on what level they are at, which is extremely helpful. At a lower level, you can diffuse with humour or just correct without making it into a challenge (e.g. they say GET ME A DRINK NOW and you say OK! I can get you a drink, but, I'd like you to ask nicely.) or just ignore behaviour but kind of notice that it's happening and steer them into some activities which will help. Whereas at some more extreme levels it's more about de-escalating and keeping everyone safe and holding a boundary about not letting him hit his brother for example, and as far as possible not letting him hit you either - I would do this by physically blocking his hands or sometimes holding him in my lap facing away from me. But the other thing which is helpful about the levels is that like when he said he was calm - he had probably gone down to a calmer level to be able to say that. But he wasn't right at 0 again yet which is why he tried to hit you when you went in.
OK - actually I have just noticed the time so will pause there because otherwise I'll be here all night. But I will come back and put on some more resources tomorrow or the next day.
The other things we've been advised to do are to focus on structure at home so make everything as clear and predictable as possible, because uncertainty will increase anxiety which increases the stress response. You can't remove all uncertainty so it's just about removing some of it. And also for us not to try to rescue him from things, including his own feelings.
And I have also noticed that a lot of the time, when I notice a lot of the little signs showing he's dysregulated at a low level, it's because he really needs to go to the toilet but he has been ignoring it for so long. Instigating a before-bed-everyone tries for a poo routine (started for the 3yo for potty training!) has actually worked wonders in our house.