There should be 3 photos there, I hope you can see them. One of the tree as a whole, a closeup of leaves, and a closeup of the bark. It is the bark that is most fascinating to me, it consists of many peeling layers, so that when you squeeze a branch the outside feels kind of spongy, with a solid core. The bark also feels damp, as if it is storing water somehow (and believe me, it hasn’t rained here in months).
My tree expert friend suggested Brazilian Pepper Tree, but the bark on that seems totally different (based on images I can see online).
Depending on where the melaleuca is growing, it will absorb heaps of ground-water, so are a very useful plant/tree to have around boggy areas and their flowers can be just delightful. But asnearwildheaven mentioned, the trees have become invasive down in Florida when they were introduced into the US to help waterlogged lands around the Everglades.
Oh, and the reason the bark and tree felt damp was because the bark and tree are full of water. Even though the ‘paper’ bark looks brittle, it’s really quite smooth and lustrous because of the moisture content.
So, my assumption was wrong. Our organization’s tree ID expert identifies it as a polylepsis australis (aka tabaquillo or queñoa), which originates in Argentina (I believe in this context, “australis” refers to “southern hemisphere”). Apparently, the original forests of this tree in Argentina are an endangered ecosystem.
Similarities in the bark characteristics notwithstanding, polyepsis australis is not closely related to melaleuca trees, being of a different Order (Rosales vs. Myrtales).