it certainly indicates the very unique characteristics that moonlight has and how those characteristics affect plants that bloom without sunlight (at night time).
The picture you originally posted calls them "night" blooming flowers. As has been explained, they have evolved to bloom at night to coincide with nocturnal insects which pollinate them. Nothing to do with moonlight.
moonlight is uniquely different than sunlight. (Moonlight is NOT reflected sunlight.)
No it isn't and yes it is. Why on earth would the moon have phases if it's self-illuminating? Phases are a characteristic of a body being illuminated as are shadows. I took this myself:
I don't have a fancy camera but even on that you can see shadows of craters, it's clear the moon is being lit.
Lunar cycles do have an impact on some things but not because there is any inherent different quality about moonlight. There isn't. It may be that the amount of light the moon reflects, which varies with the moon phases, may have an impact on things.
Just to specifically respond to this part:
What we do know is that moonlight, while generally similar to the sunlight..., shifts a bit towards the infrared...This makes moonlight not just a less intense version of sunlight—it is somewhat qualitatively different, too.
Any body when reflecting light will absorb some wavelengths and reflect others. That is literally how we see colours. There is no inherent "redness" about things we perceive as red, they simply absorb other wavelengths and reflect red ones. So yes, the light coming from the moon will have a different spectrum to that coming from the sun because of the wavelengths which the moon absorbs. But moonlight doesn't "cool things down" (another claim oft repeated on here), it's just a reflection of the light from the sun, the moon phases and shadows we see on it prove this.