I think someone is going to need to run something like a graphic analysis of an output from an HDMI port on a Mac with an M1 processor in order to compare to other apps which do not seem to be exhibiting this problem.
Ultimately, this is probably pointless. The 'problem' is very likely related to the M1/M2 48 kHz HDMI audio limitation and resampling being used to workaround it. Remember, the Apple Silicon-based M1 and M2 Macs are limited to 48 kHz over HDMI and you have to resample everything that isn't 48 kHz to 48 kHz in order to play it back. You can see this happening in the screenshot you posted above of the audio path during playback. Other apps like VLC, Apple Music, etc. the resampling process is very likely handled by the macOS system mixer itself silently (without ever informing you). Media Center on the other hand handles resampling itself with either SSRC which is the default, or the SoX resampler if the option is enabled. SoX should pretty much be the best resampling algorithm available but it seems it just doesn't agree with your ears (nor does SSRC for that matter). The most important bit here to focus on is that Media Center handles resampling itself, either through SSRC or SoX. I don't believe there's a way to allow the system mixer to do it instead, *maybe* using the default CoreAudio output with exclusive mode disabled? I doubt it, but I digress...
The *only* way to avoid the resampling completely is to use another connection that isn't HDMI whether it be USB, optical/coaxial, DLNA if the receiver supports it (and hopefully supports gapless playback), etc. This is a well-known limitation of the Apple Silicon-based Macs since the M1 was released several years ago, which Apple didn't address with the M2 Macs. Maybe M3? Or maybe they don't care at all about it. *shrugs*
What is interesting is that I hear this problem with other players which try to service both Windows and Macs. The players where I do not hear the problem are very Mac specific.
On Windows are you using HDMI out from a device (e.g. GPU) that's limited to 48 kHz only? Because being able to install Windows via Boot Camp on M1 and M2 Macs doesn't exist so that can't really be tested unless you have a PC with the same 48 kHz HDMI audio limitation. All the HDMI outputs I've used on PCs (both with dedicated graphics and integrated graphics, even the Raspberry Pi) aren't limited to 48 kHz like the Apple Silicon Macs are over HDMI and thus no resampling needed. You can verify this in Media Center via the audio path, and it'll tell you if resampling is being used or not.