Lost World.

What's the story behind the mysterious trees BangSul planted in his garden?

He hasn't mentioned it to anyone yet, for one main reason: he doesn't want LianBi to find out how he often visits the Wilds, thinking that he would panic about it and obstacle him, or even put people after him, when he wants to go there. Because he needs to go to the Wilds from time to time, that's the Temple of Isseiner, he has to feel his presence close from time to time.

It's in the Wilds that he obtained the seeds of the four trees and it wasn't a case. He was lured to a secluded area of the wilds, he had to defeat the guardian to prove it was really by Isseiner's Will that he should take those seeds.

The four trees represent 4 of the ancient races of children of Isseiner that went extinct due to the repressions of the Empire throughout the centuries: kitsune, dryads, jinglings and fairies. The trees aren't just symbolic totems, they are actually the instruments to bring these races back to the world. And since BangSul was so desperate about making his sister immortable and less delicate, what a better occasion for Isseiner if not this, to entrust the seeds to his Avatar?
Of course the God didn't tell anything about what the trees are and what they do, he just they were his gift for him, for the service he made to fight against Mijhatev, and told him to plant them somewhere safe.

And what's with the weird happenings involving BaeBee and PanAn?
They ate from the trees, but they hardly even remember. They have some sort of hypnotic effect when a 'potential candidate' gets close enough. The trees produce one fruit at a time that can't even be seen by the people who aren't compatible with the races or that aren't destined to get the transformation. In other words, it's daddy Isseiner who decides.
The person doesn't even need to eat all the fruit, one bite is enough to trigger the transformation. And it normally follows some hours of unconsciousness, depending on how much 'work' there is to do to change the body.