Before moving out to Utah in 2015, I worked for Blue Cross Blue Shield of IL in the hospital reimbursement dept for a decade.
Yes, insurance companies are definitely making bank but mostly through volume rather than profit margin. Setting aside nefarious activities like baselessly denying claims to boost profits (although I'm not denying that kind of thing happens), most insurance companies operate on ~3% profit margin. In 2018 (the most recent data I could find), US healthcare spending was $3.6 trillion. Roughly 90% of Americans have health insurance, so that would translate into $3.24 trillion going through insurers. At a 3% profit margin, that would translate to $97 billion in profits.
In terms of pure profit margin, hands down it's the pharmaceutical companies. They gouge both the insurance companies and hospitals. Their counter-argument is that they need high margins to cover their huge R&D costs, which is true but . . . they are still making bank.
You've got 5 main groups of players in the US healthcare world: insured Americans, uninsured Americans, insurance networks, physician networks, and hospitals. Everyone's aware that insurance networks negotiate rates with physicians and hospitals, but the hospitals negotiate with the physician networks as well (i.e. the primary and specialist docs who don't work out of a hospital). If you're in a metro/suburban area and you don't pay those physicians market rates, they will align with another hospital and send all their patients there - leaving you with basically emergency care only. And of course, all of these networks who are negotiating do so through administrators. And here again, you need to pay your negotiators market rate or they go work for the competition. Last estimate I saw was that 31% of all health care costs go to cover administrative costs.
So in many ways, hospitals are squeezed just as consumers are. They have to pay market rate for their employees, get squeezed from the government, insurers and physicians, and can't turn away anyone in need of emergency care. That includes a lot of uninsured, who generally can't pay the astronomical sticker price of a hospital stay. And when the uninsured don't pay, those bills wind up going to the state - who pay pennies on the dollar. Much later on.
The present issue for hospitals is cash flow. They submit claims but don't get reimbursed from the insurers/government until 30-90 days later. So they've been dealing with a huge influx of patients and those associated expenses over the last 3-4 weeks, but haven't yet received most of the associated revenue yet.
So to answer your question - the people making bank are the insurance companies, pharmaceutical companies, and the execs/admins for the hospital and physician networks.