Its backing by a stable economic and governmental system
the only real backing the dollar has is that it's the only currency you can use to pay US taxes
1 is necessary for 2, so 2 isn't really a separate point
Tokyo, Lisbon, and Santiago don’t hold debt and equity in USD because Phil from Bozeman paid the IRS in that currency.
They hold debt and equity in USD because USD is stable because there is always a Phil from a Bozeman who needs to pay their taxes, so they money will always have value to somebody