"Does the IRS have authority to issue such requests to foreign banks?"
issue requests, sure.
and companies with an international presence or countries with a working relationship with the US would be happy to respond to the IRS at least in rough confirmation.
4 out of 5 people in the US would never have to worry about making more than $125 k a year, but if you're reporting $60,000 annual income and then buying a house every year, the IRS would start looking into it.
irs interest depends on how large the income disparity appears to be before they start officially investigating and probing for more certain corroboration and confirmations.
it's just like your taxes in the US.
If you have a yard sale and don't report it, the IRS isn't going to pay attention to the extra $200 you didn't report that year unless you
happened to sell a personal boat later that year for 200k.
it's all about what flags the interest of the IRS.
"How would the IRS even know what foreign bank to issue these requests to?"
If you have over 10,000 usd abroad in total, all foreign holdings included, you are required to file what is called an fbar that year, which really is I think five fields on one form, you fill out the name of the Bank, address, the country and the amount.
that's so the IRS can keep tabs on. approximately how much you're making versus how much you say you're making if you're keeping your savings overseas.
"...gets tracked on a per-individual basis."
No worries, these are all great questions and I'm treating them like a refresher course.
The IRS is largely dependent on self-reporting whether us citizens or residents are inside or outside of the country, which largely works because maintaining a believable fiction about your income is not easy to consistently pull off and consequences for self-reporting income incorrectly are so much higher than the amount of taxes most people are going to pay that it makes sense to self-report as accurately as you can.