I have hesitated to write something in this thread on the subject of Delta Sigma chips. I don't want to be misunderstood because I am a great enthusiast of Taiko Audio. The ingenuity of Emile and the excellent build quality of all the equipment is a role model for me.
Since the discussion about upsampling continued here, I would like to make some suggestions from a technical point of view.
Emile understood the question behind the question right away, of course.
In order not to bore readers who are not interested in technical details, here is the:
Short version
There is no such thing as bit-perfect playback from delta-sigma DACs! This is because each of these chips contains an interpolator with digital filters and a modulator, which converts each PCM file (e.g. 44.1 kHz) into a bitstream. This bitstream is then DSD.
The filters and modulators in the chip must be designed with simple algorithms due to the low computing power. Therefore, every Delta Sigma DAC can benefit from receiving PCM > 44.1k or DSD as source material in order to bypass the internal (simple) oversampling.
Long version
How does a delta-sigma chip work? I did a bit of research and it seems that the Olympus I/O XDMI DAC module contains a ROHM chip.
Let's take a look at the block diagram of a BD34352EKV chip ‘as an example’ below. PCM as input goes via Audio Function Control to a FIR filter. With this filter, for example, PCM 44.1k is up-converted to 352.8k or 705.6k. In a second step, oversampling to the modulator rate takes place. This is, for example, 5.6448 MHz (16 x 352.8 kHz). This corresponds to DSD128! The bitstream generated by the delta-sigma modulator is then converted into an analogue signal.
It is interesting to note that DSD as an input completely bypasses the internal oversampling of the ROHM chip, as it is already available as a bitstream.

Source:
New 32bit D/A Converter IC for Hi-Fi Audio Equipment | ROHM Semiconductor - ROHM Co., Ltd.
In order to bypass the chip's internal oversampling, external upsampling with higher precision (e.g. floating point instead of fixed point), better filters and higher quality modulators can be used. DSD requires very high computing power. And here Emile is of course right that more power = more noise and interrupts have a negative effect on the sound. There are strategies for this. For example, you can buy high-quality DSD as source material. Or you can do the upsampling with another computer using software such as PGGP or HQPlayer.
Summary
Taiko Audio is designed for bit-perfect and noise-free signal processing. Anyone who buys this device should operate it exactly as the manufacturer recommends.
In my opinion, the Olympus ROM DAC-Chip or your DAC can also benefit from upsampling. But I would either buy DSD as the source material straight away or convert it to DSD online or offline using another computer. Because the Delta Sigma chip does it anyway, only with presumably worse algorithms. These chips are widely used, e.g. ESS Sabre DAC chips, AKM, ROHM or Burr-Brown.
Neither the Olympus nor the DAC recognises that the material is upsampled. Instead, both treat it as ‘bit-perfect’ source material.
Whether this really sounds better is something that everyone can decide for themselves. With my contribution I want to give a suggestion as to why upsampling can improve the sound and what the technical background is.