You are correct I really don't understand it. I had retiree health insurance when I retired but before Medicare, it cost ... more, maybe $400 a month for me? I don't recall. Once I turned 65 the cost went way down. As you note, it seems to work. I get a statement each year from the company about the finances of retiree health care. It costs the company some money.
My real point is that IF you retire early, this is a significant consideration.
What you're describing sounds like supplemental. I'm just guessing, but it seems that you kept company insurance after quitting, and that's what you're calling "retiree H.I." When you started Medicare, you must have continued the company's insurance, which then shifts from primary insurance to secondary, supplementing Medicare Parts A and B. (A is hospital, B is doctors visits, basically.) Company insurance gets a lot cheaper in that case because Medicare, as the primary insurer, is lifting most of the weight on any bills you incur. Many companies offer the option to continue insurance with them as secondary behind Medicare. I can tell you from working at a clinic dealing with patient insurance, the people who can afford that and do it are indeed sitting pretty. They basically don't pay for anything beyond their premiums. Exceptions can occur, of course.
Medicare Part C is those Medicare Replacement plans you might see advertised on TV. Each area is going to have different companies administering those plans, so the names and companies where you live are probably completely different than what's around here. It effectively replaces Parts A, B, and usually D. The upside is premiums can be $0, which is why a lot of people do them who can't afford Medicare. There are downsides, and I've seen plenty of it. Those plans made up a huge chunk of our patient base when I worked at the clinic. They'll make you jump through way more hoops than Medicare, both for annual checkups and for authorization for any tests/imaging you might need. You'll also be limited to in-network providers (okay, actually everybody is, including Medicare, but most all clinics accept Medicare), and your network is usually limited to a specific area. So, if you travel a lot, those plans can get tricky if you need medical care when you're, say, prancing around 4 states over. The biggest downside to those plans from my POV is finding doctors that take them. Increasingly, it was harder and harder to find specialists who accepted those plans. Really screws with those old people who use those plans. BUT, they are cost-effective.
Medicare Part D is for prescriptions. What pays for stuff at the pharmacy, etc.
I've never messed with a HSA. If I stay put and work as many years as I expect to, the state will pay 100% of supplemental premiums if I elect to keep their insurance in retirement (secondary to Medicare). In the meantime, the state pays 100% of my premium now, and a big chunk of my wife's, which, given my health over the last 15+ years, is a big consideration for me keeping this job.