Yes it will be paid by the government, but the aggregate expenditure will be lower in part because of Medicare’s bargaining power.
Nothing is “free” but there are more and less efficient ways to organize economic activity. Just like if you have 10 units, you can multiply 8x2 and get 16 or 5x5 and get 25. Those extra 9 units aren’t “magic”; they’re the product of efficient organization.
Okay, we can make the payroll tax progressive. Sure. We can also just abolish it. I don’t understand why you are insisting this program needs to be “paid for” by either taxes or interest-paying debt given the deflationary pressure of disrupting an industry this large. Issuing a treasury bond is literally the government borrowing money that it has already created. There’s no reason to do this instead of spending money into the economy in the form of wages for new employees and healthcare payouts. If inflation ticks up to an uncomfortable level, we can levy a tax somewhere else. Maybe wealth or something. But it’s not even clear that would be necessary.