I have an early 2015 retina MacBook Pro running macOS 10.15.5.
I also don't get sound from Chrome at 768 kHz. In Firefox, I do get sound but it's quite distorted.
Anyways, there is no reason for you to set the sample rate to the DAC's maximum. Since all the components above half the original sample rate need to be filtered out for accurate playback, all you end up doing is using the oversampling algorithm of macOS's Core Audio rather than that of the DAC. Thus, it is likely best to set the sample rate of the DAC to the original sample rate of what you want to listen to.
Regarding the number of bits, Audio Devices tends to only show the maximum number of bits for USB devices. If the DAC's sample rate is that of the audio file and the volume is set to full, it will not add or subtract anything, i.e. the least significant bits are all zero.