Just like cash, the central bank would issue it and, depending on the actual design, private individuals as well as retailers and other companies could pay with it. It all boils down to trust. A CBDC available to all citizens would ensure the stabilising effect of central bank money in payments.
One key criterion for confidence in our money is that people can exchange money they deposit with their commercial bank at any time, at face value, for central bank money. Public money is therefore the anchor of a well-functioning payment system and ultimately ensures confidence in the stability of our currency.