Hi
I’ve used the Up2Stream V3 mini in a few projects and haven’t had a noise problem. I’ve generally powered mine with DC-DC or AC-DC converters too, an example is in the circuit diagram on this page: Cambridge Audio A5 Amp with Arylic Up2stream Mini V3 Streamer
In the Cambridge example, the wifi and bluetooth aerials were fitted directly into the chassis of the amp. It’s a shame I don’t have a spectral plot to show you, but would have measured it and I’m fairly sure there was no noise.
Be careful you don’t assume you won’t have an earth loop because you’ve not got a mains earthed PSU. The loop could be elsewhere.
To fault find, I’d start by testing the Up2Stream V3 module on it’s own with headphones to see if that has a problem.