Ok then same noise if the dac is not connected to the amp just the speakers,
Then when it’s switched to XLR input (which is .5db lower gain than SE) as Stereophile measured, it has more noise to you from the speakers, it must be a Balanced to SE summing opamp giving the extra noise, and therefore should not only be quieter using the SE as you found, but also sound better because the summing opamp is not used.
I found exactly the same but other way around using Belcanto Ref600 monoblocks, the RCA input used a se to balanced opamp into the Hypex NC500 balanced input buffer module, the XLR input input did not use it and had the same gain, and not only had less noise but sounded better as well (less hifi’ish), because the opamp was not used.
Cheers George