iirc the experiment was verifying that anti-matter falls downward in gravity? otherwise it still functions physically rather like time-reversed matter. Unless anti-matter is time-reversed and has reversed gravity in which case it would also seem to obey normal gravity because we would see it under the effect of anti-gravity but backwards?

Isn't that the opposite of what we're "seeing" now with the expanding universe and dark matter (not anti matter) being the reason for space to grow?

Anti matter and matter live inside the space, that dark matter is "producing"

At least that's my layman interpretation of looking at some videos and reading some stuff

So, I have no clue ;⁠-⁠)

Don't know about that
Can you provide me some more words to search for it or even a link?

Yeah, CP violation is a big focus when it comes to the research of baryogenesis, the theoretical process that produced the baryon asymmetry! Her experiment established that parity symmetry (P) can be broken through weak interactions, and later experiments showed that the combined CP symmetry (charge conjugation + parity) can also be broken, again through weak force shenanigans.

CP violation is one of the three Sakharov conditions (which were proposed by and named after Soviet physicist Andrei Sakharov) of dynamic baryogenesis, as it would mean that matter and antimatter can behave differently in certain processes. If they behaved identically, no asymmetry would be produced and they would both annihilate. However, there was one extra baryon for every million antibaryons (we know this through measurements of the CMB and the quantities of light elements produced in Big Bang nucleosynthesis), and this slight difference allowed matter to dominate the universe.