Could the desaturated look be a result of the streaming compression?>
No, compression or resolution won’t affect saturation.
But HDR vs SDR colorspace and brightness will make a difference.
SDR has a smaller colorspace, so it’s less saturated by definition.
Seeing the screenshot comparisons between the 19SE and the 04/11 reminds me in a big way of the differences between the old blu-ray of The Matrix (which, it’s worth noting, would’ve also been from an hd master created in 2004 just like the OT blu-ray) and the remastered-in-4k blu-ray included with the UHD release.