OP, I have to say, I was very worried by your first post but as you give more detail, I feel like this is more behavioural based and also based in a certain fantasy of how you want being a mother to feel …. Both those things can be worked on.
behaviourally, we all have different behaviours that trigger us. Sounds like you are not triggered by tantrums but you are by chaos and lack of emotional connection. Your fantasy about communication with him (quietly sitting, listening, while you help him speak) is a very unrealistic one, especially for a five year old boy. It sounds like you have some basic irritation that he’s almost obliviously bouncing round the place making noise (the opposite of your fantasy, which he seems to be spurning!) While you may have one or two moments like your fantasy with both your children through the decades, they tend to be few and far between.
I would suggest become aware of your fantasy and triggers and analyse them a bit, and let go of them as best you can (or take responsibility for them atleast). Eg for me, I was triggered by whining. While I found defiance no big problem. Why whining? Because I never allowed self pity in myself. It was a forbidden emotion in my own childhood.
for you, you mention self consciousness about what people think…. Maybe you are someone who never allows themselves to be noisy or boisterous or catch attention, who thinks everything needs to be restrained/ordered. Your son, who does all this effortlessly and unapologetically- without your permission or help, could actually feel threatening to your own coping mechanisms/ world view.
Anyway. My other suggestion would be to not let it get embedded in your mind as a permanent judgement. Ie don’t tell yourself “I have a favourite child”…. Otherwise that will become permanently true. Say to yourself “right now, at this age phase, I find DS’s behaviour more triggering/ harder to deal with, so I need to take extra breaths with him, and find ways to counteract that, so we can have positive connections’”.
good luck.