It's just volume. Mismatched extreme cases of impedance can slightly alter the sound, usually for the worse by adding slightly extra bass. My powered Roland workstation's headphone jack is an example, it gets incredibly loud easily and makes some headphones bassier. Not desirable and an extreme case out of dozens.

Out of all the audio interfaces, amps and even dongles I've used in shops, studios and from home, they basically sound the same, just can deliver different volume.

Soundstage widening, extra detail, cleaning up frequencies, all of that I don't get and even if that was true, it's going to be a result of it altering the frequency response of headphones which is a bad thing. I don't want a coloured amp, I want an accurate amp.

Save your money in this marketing speak dominant hobby.