I had the same college experience. I nearly raised my hand to request permission but saw other kids just leaving class (sophomores I think)
Business school classes were very much like high school, at least the ones I took (I was not a business major). Assigned seats, attendance taken, etc. Don't recall if bathroom trips needed permission as I always handled that before class started.
Math and science classes were generally much more informal. Class met at a specified time and place, and nobody paid much attention to who was there or not. I would occasionally sit in on other classes I was considering taking, to see if I liked the instructor.
At my university, attendance at lectures and tutorials was optional and no attendance was taken (for most subjects). Most people went to the lectures but attendance at tutorials was much more mixed. I tended to skip tutorials a lot.
I remember one year I promised myself "This year I'm going to turn up to everything". So I went to the first tutorial for one of my CS subjects. The tutor asked us "Is there anything you didn't understand from the lecture?" We all said "No". He said, "Then why did you bother coming to the tutorial?"
Then he told us he was trying to teach himself quantum physics as an excuse to not work on his PhD thesis. He asked us if anyone knew quantum physics. One guy in the class was a physics major and offered to give the tutor a quantum physics lesson. The rest of us just left. And the tutor would have put that down on his timesheet and got paid for it.
I didn't bother going to any more tutorials for that subject.
In hindsight, maybe I should have complained, I probably could have got that tutor in a lot of trouble. But I didn't.
Might be good you didn't. I obviously don't know the particulars here, but I've learned that the attitude of the university teaching staff can be confusing because of non-obvious job reasons.
At my university, there was this PhD having labs with us who I liked - she seemed one of the smarter and wiser of the people I've dealt with up to that point. A year or two after those classes, we ended up having a discussion about upcoming changes in the curriculum. I asked if she'll still be running the same labs she did with us, at which point she almost burst into tears and said something like, "oh god I hope not". I was perplexed by it, until she explained to me that she never wanted these labs, she was forced by her superiors to run them, and they are completely unrelated to the domain of her research. That insight made me understand several other cases of PhDs and professors that seemed incompetent and/or disinterested - it's not that they were bad or stupid; it's because the university mismanaged them into teaching things entirely outside their domain.