The noise origins from the PC and is transmitted through ground/shield connection to the Burson Conductor.
ADI-2 is just an inter-step on that path, in a way that doesn’t change with Firmware.
Else I would recommend to install an earlier FW.

Maybe you dial the Burson’s volume more up now, having ADI-2’s Volume more down.
What’s your typical ADI-2 Volume AND Ref. level, in dB or dBr (r indicates Auto Ref Level is on).

Things you can do, in order of relevance / effort:
• Dial up ADI-2’s Volume, dial down Burson.
• Install a ground wire to one of ADI-2’s screws.
• Use an USB isolator.

Ground wire example:
https://smile.amazon.de/Warmbier-Erdung … amp;sr=8-2

Your levels are fine, nothing to optimize in this regard.

Would be interesting if the noise is still there if you turn the Burson’s volume all down.
Seems there’s a whole family of devices, which Burson Conductor model exactly do you have?

Anyway - the probable solution is the grounding of ADI-2, e.g. on a case screw or the silver D-Sub-9 locking screw.
This should deduct the noise current away from the Burson.

If you have some wire you can test it, but please don’t stick the wire into any mains outlet’s hole, to avoid being electrocuted.
Use any metal cased grounded device to temporarily pick a ground connection.
You can even try case-to-case contact, grounded device to ADI-2, for this test.

Only if nothing else helps go for an USB isolator.
These don’t come cheap and tend to cause other problems.

If I get it right this thing is headphones only amplifier.
I was in the obviously wrong assumption you are using speakers with it, because some of the Burson offerings have speaker outs.

Why not just, for the moment, use ADI-2’s headphones out?

But you don’t have speakers connected, right?

I wouldn‘t worry about possible noise issues for future amps.
Each amp is different and reacts differently.

The fact that the noise does not go away when you bring Burson‘s volume all down clearly points to it‘s less than ideal construction, regarding the internal ground path.

Compare that to ADI-2, which has to suffer from the same ground noise current running through it, but stays completely unaffected.

Anyway, even this one could be solved, with more or less effort.

BTW, your PC is a laptop or a tower/desktop cased one?
Three prong or two prong mains connector?
The cased ones often use plastic pins for mounting the mainboard, disabling the mandatory mainboard-to-case ground connection.
A simple metal screw close to the USB connector possibly solves the noise.

I would recommend to separate this Burson of yours and ADI from each other permanently from degrading ADI´s performance. Donate Burson to Unicef or throw out of window, for example. 

ADI can deliver +22 dBU (9,8 Vrms, 13,8 Vp) of voltage to cans. It does this with impeccable headphone amplifier other properties:

-VERY large current (voltage x current = power) reserves

-VERY little noise

-VERY low output impedance.

+22 dBu is a very large signal level (voltage) for headphones. Most normal headphones can´t even handle this much i.e. their drivers clip or they distort otherwise earlier or much earlier. Distorted or not,  the end result (sound pressure level) by putting +22 dBu to any headphone, is ears blowing.

So one does not need to be particular Audio Einstein to derive the audio relativity theory -level circle conclusion that ADI DOES NOT NEED ADDITIONAL AMPLIFIERS for headphone use in 99,5% of use cases.  It does so in case of passive SPEAKERS only. For line level operations, i.e. for headphones and active speakers, its fully armed driver by itself.

Most likely practical consequency of hanging extra amplifiers to ADI´s ass is massive penalty shot to its excellent SNR; ADI´s ~115 dB SNR values are definitely gone. Plus very possible ground-loop -related extra problems, like in your case with this Burson.

Now as a sign of amendment, show your ADI the esteem it deserves: by giving it the full and exclusive amplification & playback responsibility in your headphone system.

You too happen to have extra headphone amplifiers in conjunction to ADI? How many chained amplifiers you have, in total?

Record I have seen is ADI + three (3) additional headphone amplifiers in a row. It went something like this

ADI ---> fore -headphone-power-amplifier ---> secondary -semi-final-headphone amplifier ---> the-final-stage-primary -headphone amplifier

If ADI could start drinking, it would definitely do so in these cases...