Hey man , loved your post. I found it by googling symptoms I had as a kid. I would repeat sentences and your the only person that ive ever heard describe that feeling of "brain being satisfied". I can relate to it. I used to do this thing where I had to touch something in groups of 5s, and then do that too, 5 times. Then if I messed up I could backspace. Until I hit 50 or 100 or any other satisfying number. I caught myself doing it, and I remember seeing myself in 3rd person and kind of forcing myself to stop mid-counting(example: stopping at 12 or 17 even though my brain wasnt satisfied) and doing so consistently eventually made those habits disapear.
Id also make people repeat themselves whoch got on the nerves of my familly and babysitters. If I heard them say a sentence but something in my brain said I mightve misunderstood, I absolutely had to hear it again from them, PRECISELY as I thought I had heard it first. Almost to confirm or reaffirm that I had understood. You seem to have the same thing as me , a deep fear or aversion to being misunderstood or misunderstanding in general. Anyways I asked them to repeat and threw fits if they didnt remember what they had said or if they reworded their sentence. That stopped because my whole familly disciplined me when I did it just like a child who hits or bites or says bad words. It worked. Although I still hate being misquoted.

I also quit smoking, cold turkey as you have. You have to watch yourself like you're watching a toddler thats gonna hurt itself if left unnattended. Like "hey, get your hands away from there! Careful with those scissors!"

Anyways I wanted to tell you all this in case you relate and makes you feel better. Also you can certainly stop that behaviour, or atleast, try and limit yourself when you catch yourself. Anyways, best of luck friend, best of luck friend, best of luc... Just joking , cheers !