I bought a Snowsky Retro Nano (I paid $59.50). Snowsky is a (new) sub-brand of FiiO, they also have an entry-level DAP (~$50), and an on-ear headphones (~$18).
The Retro Nano is a Bluetooth/USB battery-powered dongle. It has both 3.5 and 4.4mm outputs and I believe it is closely related to FiiO own’s BTR13: it uses the same dual CS43131 DAC/Amp (pfff..... I'm not off-topic this time!

), and a QCC5125 as USB bridge & BT receiver. The complete spec, including FiiO APx500 measurements, are available at:
https://www.fiio.com/retronano_parameters
Here it is, with the BTR13 and Qudelix 5K on its right:
It’s a cool device!

I like the retro “cassette” look (it's an animation!).
It has a removeable 10440 (450mAh) battery—easy to replace when dead, around ~$3 a piece. But you can also increase the autonomy by carrying a spare (charged!) battery(ies). A battery container is included. Oh, and it also works with no battery, powered from the USB port.
It is not yet (?) supported by the FiiO Control WebApp, but the FiiO Control app (tested with iOS) enables quite a range of settings, including a 10-band PEQ (up to 3 custom "sticky" PEQ settings—they are saved onboard—plus the usual Jazz, Pop, Rock, etc.). It’s not quite as comprehensive or "advanced" as the Q5K app, but it makes for an easier experience overall: for example, all the main settings are accessible from the on-screen menu, so most of the time, you don’t need the app at all.
Ok, now my real CS43131-related question… The app offers these two THD compensation sliders:
The BTR13 does not have these... I have seen comparable features on ESS DACs: for example, the E1DA ESS-based dongles expose similar H2/H3 comp. settings in the app, and the corresponding registers are documented in the ESS datasheets. They are intended to "compensate" (some of) the THD generated in the I/V stage, potentially the amp. stage, and even the Headphones or IEM... On E1DA dongles, you can also use them the other way around to purposedly add euphonic THD (I suspect some OEMs use this trick to create their own “house sound”).
But this is the first time I see a THD compensation on a Cirrus Logic DAC. I could not find any mention of THD-comp. registers in CS4313 datasheet either...
Is this an undocumented feature of the CS43131? Or, is this something FiiO implemented in the QCC5125 Kalimba DSP core (I believe it's relatively easy to do in a DSP)?
EDIT: The Android version of FiiO Control app does not show these THD comp sliders when connected to the same Retro Nano device. I then looked back at the iOS app, and these sliders are actually stuck to zero. Why do they even show up on the iOS app... I don't know!
Oh, and before somebody asks: are these H2/H3 comp. audible?
Maybe… So far, I have refused to drag my immediate family & friends in this hobby, meaning I can’t really perform a valid controlled blind test on my own! EDIT: totally inaudible !!! It's embarrassing, but I just realize that, in my haste, I was moving the channel balance slider around and not the second-harmonic compensation slider.

So, now the (updated) correct, question is: is the channel balance setting audible? My (updated) answer: Maybe... If I change this balance setting enough !!!