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Surely an electronic wrist watch is fine, and maybe an mp3 player. Also graphing calculators.
Do graphing calculators actually help people learn? We used them in high school, but when i needed to take calculus in university we didn't use them. I'm doubtful they are good for learning especially when trying to teach the foundations.
Complete waste for anything math related for me. Did act as a proper gateway into coding though!
I distinctly remember writing a minesweeper game, using the built-in programming language. Not the fast compiled one you needed a cable to transfer! Just button presses.
Same for me. Felt like a superpower.
Personally, playing with the graphing and algebra functions on the calculator were hugely informative. Rapidly trying out different things, seeing how they looked how tweaking things would cause adjustment, all added educational value.

I feel like graphing calculators enable exploration in a way that doing it manually with pen and paper cannot. Obviously, pen and paper is super valuable as well, but I feel that they are complimentary.

Back in the day the feature I liked most about my TI-82 was the amount of information that could fit on the display, the formatting options available, the ease of entering and editing what you entered, and the amount of past entered formulas that would be saved and how easy they were to retrieve. It made doing large blocks of basic BEDMAS math very quick and less suspectable to errors caused by accidentally hitting the wrong key entering in large formulas, and very easy to go back and find out where I messed up and quickly retabulate everything.

All of that mostly comes up in physics and chemistry were its about knowing what long formulas you need to plug the numbers you have available to you to find out what you need to know. Oddly enough their seems to be very little benefit to using a graphing calculator in a actual math class.

> BEDMAS

I think I figured out what the B stands for, but where I'm from, we call it PEDMAS - the P standing for Parentheses.

It really depends on the level of the class and the goals. Usually by the time you're getting to calculus you're moving away from simply calculating a numerical answer anyways and the problems where you do need to find one just to test that final step can be finessed so they're simple to calculate by hand and eliminate the problem of full computer algebra system calculators that can handle the symbolic manipulation too.
In my case it did. I took "advanced math" (trig, mostly) in high school from an abysmal teacher. Ignoring her and developing an intuition through graphing was the best thing ever. I had the best final grade in the class.
They were brilliant in electric engineering classes. I found these calculations very tedious.

For maths not so much, as it was less about providing a numerical answer, and more about understanding the question.

I don't see the need for it. The only time I ever needed to graph a function was to answer a homework problem that specifically asked me to. Having your calculator do it misses the point.
Why do you need a music player in school?
"Need" might be strong, but I am okay with music players. My ADHD self is able to focus many times better if I have certain kinds of music playing to block out nearly talking and other distracting sounds.
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This was some 20 years ago, but

- iPods? Taken away

- didn't have fancy smart watches, so those were fine. But I'm sure a modern smart watch wouldn't fly

- graphing calculators were fine. Just don't make it too obvious you were playing Pokemon Red on it.