Banknotes are loans to commercial banks.
Yes, but banknotes
alone don't create debt. While commercial banks do borrow money from the central bank, the money the central bank creates is out of thin air. They represent nothing.
Yes, there's lending between the central bank and the commercial banks and yes, there's lending between the commercial banks and the households/businesses, but that doesn't show that the dollar, as a unit represents a "thing", as you put it. All I see is trust from the commercial banks and households/businesses to the monetary policy of the central bank, which is controlled usually by one entity, the government.
Debt are loan contracts secured with collaterals or bank capital and evidenced in the accounting books of the banks. These things do exist. Math symbols on banknotes or deposit accounts simply informs us about the share in this debt. Check the video in the OP to see how the debt is paid to owners of that debt.