However they are working on having their own battery and battery factory design. They are even working on their own cathode manufacturing plants.
They have a very large 'pilot' plant in California to test a completely redesigned battery manufacturing system. They are actively building additionally battery factories in Austin and Berlin and have a equipment on order for these factories. For the Battery factory in Berlin they have received funding from the European Commission for this.
Tesla will not be fully vertically integrated but they will provide a large parts of their own cells and likely a increasing share over the coming years.