Lots to respond to! Let's get the sarcastic point out of the way first:
My motivation for teaching English is less lofty than most of the other people I've met.
You need to meet more. Most over here in the lower ranks have zero loft to their goals.
Is N5 a reasonable level to have to get around in Japan? Or is it so negligible it wouldn't really have an impact my ability to participate in the country?
You can get around for years with almost no Japanese whatsoever. Live/Travel in rural areas and you will need more. But are you trying to be a linguistic cheapskate here? Learn all you can for at least 2 reasons: enjoyment with less stress in daily life, improving your chances of better jobs.
Do people who taught English there feel like they developed useful skills? Not necessarily in teaching.
How long is a piece of string? What you earn & learn here depends entirely on you. JET instructors and eikaiwa drones can learn a lot if they apply themselves, or they can just drink themselves into oblivion and learn squat. Non-teaching skills? Perhaps some management skills, depending on your work situation, but they may apply only to managing certain people in certain situations.
Is there a noticeable difference in quality between teaching English in Japan, Taiwan, and South Korea? I think that's better suited to ESL cafe but I thought I would ask here as well.
I have not taught English anywhere except Japan, and my teaching experience in the U.S. is limited to a few science lab courses. That said, yes, it's vastly different in Japan vs. the U.S. I've seen research presentations and journal papers from Korea, and things look very similar between J and K. Taiwan is not all that different, too. It sometimes depends on the motivation of your students, and for that angle, Taiwan is better than J or K.
And, yes, talk to people in the Cafe. They'll remember me.
How useful is the position once you return to your host country? From my personal network I've seen very mixed results so I'd be eager to hear how it's turned out for people.
Sorry, haven't gone back, and I think this is not the place to ask.
If I were interested in a Japanese (English language) graduate program would the English teaching position help or hinder me?
IMO, neither, really. The experience of living here would be a greater positive to any grad program, simply because of learning the language and knowing how to live by yourself here.
What sort of grad program interests you? Darned few English ones over here, and the unis here are not all that respected abroad for what they crank out.
Now, let's tackle something else you stated:
I'm currently finishing up my bachelor's degree in earth science, minoring in chemistry and physics. Although my background is almost exclusively in stem, during my time at university I've developed an interest in international relations and business. From a career standpoint I've worked mainly in university and nonprofit settings. Unfortunately my skills don't relate so well to teaching or English recitation,
It's not recitation; it's conversation.
Most employers at the level you are qualified for don't usually give a hoot about your degree or background. They only want a fresh-faced, fairly young and green cherub who doesn't ask a lot of business questions but who can entertain (edutain) their clients and bring them in and keep them because they are a native speaker. Whoop-de-doo, but that's the reality. FWIW, I have an advanced degree in the sciences, had zero English teaching experience when I first applied, and got in with little trouble. Not all have that luck.
I'm moving away from STEM and I'm more interested in going the international business/sustainable development route for the future.
Have you thought of marketing or sales in a STEM company? Or an MBA? Most of the sales and marketing geeks I have run into over the years barely had an education in science, and it was more their personality and drive that kept their jobs. The STEM background just helped them to understand the company's science lingo more easily (a debatable point I won't go into).