Not OP but you do have to pay separately. Although as you say, that's a crazy amount for just 3 weeks. In my experience I was charged about $100 for two weeks of regular use + one roadtrip from Miami to Orlando and back.
Maybe it was just idle fees, that seems like it could go up by a lot if you leave the vehicle on the station:
>For every additional minute a vehicle remains connected to the Supercharger, it will incur an idle fee.