Hello
I have a Brazilian Rain Tree and I'm thinking about adding moss to the trunk and soil surface. Is that safe to do? Aside from the aesthetic appeal, does it serve any other purpose? Also, what's the proper way to apply it?

Keep moss off the trunk. The moisture rots the bark off and that is bad for the tree.

Over the soil is ok for aesthetic, that's it's purpose.
Other than that, it helps to keep the substrate in the pot or on the slate, but specially slates.

Also, you should avoid moss on the trunk, it's not good.