Looks like the compressed version is a bit sharper to me.
> The resulting image has way less detail in higher frequencies.
But the compressed version actually exposes more detail.
No. It really doesn't.
It adds a couple of visual filters (brightening, sharpening) before recompressing, but these don't "expose more detail", but rather all three steps actually introduce additional errors. Errors that trick they eye into seeing a "better" image, but errors nonetheless.
Are you attached to JPEGmini? If so, would you be willing to bet that I cannot tell if a photo of my choice has gone through your system and been compressed?