What would be the most likely reason for a post-scarcity civilization to preserve humanity from extinction and move it to different planet, along with terrestrial life that has been repopulated on the said planet?
Suppose a post-scarcity interstellar civilization controls a few hundred star systems. Because they are post-scarcity, they can easily supply their bodily needs.
Because lower tiers of their needs had been fulfilled, their society changes their priority to pursue knowledge, to learn more of the universe they lived in.
Then they settle on many lesser civilizations' planets, secretly. One of them is Earth. Their motivation is not to invade, but to study those civilizations and watch them grow.
Their external morphology is quite indistinguishable from humans' external morphology, but their anatomy and physiology is not entirely human-like (I know it's unlikely for this to happen in a species that evolved on a completely different planet, but there is an explanation for this matter in-universe, in which uncovering it on this question would be off-topic), except for skin tones, hair pigments, and ears slightly (not too pronounced like Spock's ears) pointed at their tips. This aids them to blend in human society (just put some cosmetics and they're ready to blend in) to study humans closely.
One member of their second generation on Earth rebels and reproduces with a human woman in its disguise on a human city. The woman gets pregnant and gives birth to the first alien-human hybrids (with more human-like appearances, less pointy ears, and more human-like anatomy up to some degree).
It turns out that the human's genome differs from theirs by less than 1% (really, they were surprised, because in-universe, their understanding of exobiology dictates that it is very unlikely for species that evolved on different planets to have a completely similar genetic make-ups, just like what we understand).
This sparks a wave of curiosity about humanity, and an interest to study humans more. Their public even assigns humanity with informal tag, as their sister race.
Then good things have to end eventually. As described in this question's background, another species, unaware of their existence on Earth, wages a war to take over humanity.
The aliens decide to stay neutral, and let humanity fight for itself, because they believe that even if they had the will and might to overwhelm the invading aliens, the events of humans are not theirs to intervene.
That human-alien hybrid stands for humanity in a trial to preserve humanity, held on the alien's home-world. As humanity is on the brink of extinction, his heart fonds on humanity as much as his fondness to the aliens.
Then, (move to the question above).