Okay! I’ve been waiting a long time to talk about this.
This is the reason the twins are so ridiculously OP and can do things other spirits can’t. Spirits get power a few ways. Their anchors provide some. When kilm think about, worship, or otherwise acknowledge an anchor, it provides some energy for the spirit attached to it. Additionally, spirits can go out and gather additional energy on their own in all sorts of ways. Some devour souls, some eat dreams, some may feed off of ambient positive or negative energy, creative or sexual energy, etc. Lots of options there.
However! Li and La haven’t just been doing those things. They ate (or more accurately, absorbed) Mun and Solt soon after Nox created them, and they’ve been basically using those super old, super powerful spirits as battery packs for thousands of years. Just sucking them dry like a kid with a juice box.
When one of the moons shattered, Mun was the one it truly hurt, and because he was inside Li, Li took the damage as well, while Solt and La were unaffected. For Li to survive the moon’s destruction, he had to separate from Mun. La likewise gave up his connection to Solt, both out of desire to match his twin and fear of what would happen if the second moon were to also be attacked.
And so the twins survived.