As Steve says, it is not as simple as the drivers determining the sample rate - the audio “host” API that you choose in Audacity’s Device Toolbar makes a big difference. MME host resamples everything to and from 44100 Hz, so if you choose MME you are getting the device’s current rate (if not 44100 Hz) resampled to 44100 Hz by Windows, then resampled to 384000 Hz by Audacity.
“Actual Rate” in the right-hand section of the Audacity Status Bar at the bottom aims to shows (when playing) the rate being communicated by Audacity to the sound card. “Actual Rate” when recording aims to show the rate communicated by the sound card to Audacity. Don’t rely on Actual Rate being free of bugs.
This is an extremely complex issue, but see this answer I wrote in response to a similar question Playback Sample Rate and Bit Depth? - #3 by Gale_Andrews . Unfortunately you don’t give your version of Audacity or Windows (see the pink panel at the top of the page). In principle on Windows Vista and later you can force Audacity to request the sample rate direct from the device without Windows interfering with its own resampling by choosing “Windows DirectSound” host in Audacity and both “Exclusive Mode” boxes in Windows Sound.
My impression is that the most reliable indicator of sample rates claimed to be supported by your device will be found at Help > Audio Device Info… in Audacity (look under the Windows DirectSound entries, not MME) and if you are on Windows Vista or later, in “Default Format” in Windows Sound.
Gale