Anyway, since this DAC is a 1-bit DAC, the firmware actually can impact sound characteristics. For example, in a DSM algorithm like noise floor shaping, they can tweak the order of the modulator; if they set it lower, that might affect ringing (timing artifacts), as well as the choices of dither, reconstruction filters, and tap length. I don't think we can assume linear phase and minimum phase sound the same; they might not impact tonal balance or frequency response directly, but they impact ringing and the time-domain, which humans are sensitive to, too.
That's even before we mention something that's completely off, like in Topping's own Centaurus case, where people complained it sounded 'off' somehow in some modes and Topping had to release a few firmwares to correct the issue of the phase going off, for example. And many times they don't put it openly in the change logs—you can check the A70 Pro's case, where the output changed from the 4.4 in one firmware. They didn't even state that, but they rolled out a hidden fix (without mentioning it in the changelog at all, while mentioning other issues).
So, firmware on these 1-bit and R2R DACs can impact sound, but whether that's the case for this Topping D90d before 0.40 and after 0.40, only Topping themselves can tell. But for me, 0.39 sounds much closer to the D900, while 0.57 sounds very 2D, like early Topping. YMMV.
