Correct, those 6 pins only get you power. There are 10/12-pin USB C connectors that will work for what you want. Those will have the same 6 pins as your existing connector, as well as the two pairs of D+/D- pins (two because of the reversibility of the connector, they just get tied together external to the connector), and often SBU1/2 as well. You need the CC pins and their attendant resistors to allow a USB C host port to detect the device, so the minimum for a proper USB2 power and data connection is 10 pins on most connectors -- 2x Vbus, 2x Gnd, 2x D+. 2x D-, and CC1/CC2 (there might be some connectors with the duplicated signals bonded internally to allow fewer external pins, but those are unusual as far as I've seen).