Another interesting observation, while still staying in the stock 1832C firmware: I have connected the device to the PC via USB, opened the Keysight Connection Expert application, and in the Interaction IO utility, sent the command "FREQuency 100000". The frequency changes to 100 KHz, and in the oscilloscope I can confirm that this is the frequency it is outputting.
It is worth noting that when the device is connected via USB, the output has a significant DC offset, besides being somewhat noisy (see attached screenshot).
After removing the USB cable, the 100 KHz setting remains active until the power is cycled. The sine wave in this case is clean and has no DC offset.
Cheers