All debts public and private refers to debts by a creditor. A drink you haven't paid for isn't a debt. It's just an account payable. They don't have to take your cash.

>debts by a creditor

It's clearly not all debts. I actually can't think of any debts this applies to. Your student loan, credit card, auto loan, home loan, water bill, power bill, heck even rent if you're in a modern corporately owned complex... would never under any circumstances accept cash payment. It would be stunning if one even provided an address that isn't a PO box, let alone an address where you could get in the front door if you showed up in person, assuming you were willing to travel a few thousand miles.

At most there might be something like a retail bank branch where you could deposit cash and then request an electronic transmission of the same amount of money.

Pretty sure they can:

https://www.federalreserve.gov/faqs/currency_12772.htm

Or, just exercise their right to not serve you? If you order something and then are unable to pay in the manner they request, they can just throw the drink away and move on. This would also happen if your card was declined.

I used to think that but after some more reading I realized it’s fundamentally not true.

YANAL, as you said, and this is a common misconception about what “legal tender” is.