It looks like Mesquite to me. I had a buddy in Texas send me a box of Mesquite and for the most part it's this tan color, but there were some darker pieces that almost resembled Walnut. He confirmed the entire box was mesquite. If that's bark on the first photo, right side, that doesn't look like any Mulberry I've ever seen. The bark is usually much smoother.
My first run-in with mulberry was in Japan. (Mulberry trees were big at one time as that is the tree that silk worms were cultivated in for obvious reasons.) I would frequent a home center that had slabs of wood. I kept seeing one that looked like walnut. While I was fluent in conversational Japanese, I didn't know all the technical words of most trees. I asked what kind of wood that was and a helper said "Kuwa". I wrote that down and went home an looked it up - Kuwa = Mulberry - the silk worm tree. We had a few mulberry trees in the woods around our farm that I grew up on in Mississippi, so I was happy to learn that. I purchased that slab, about 2 ft X 3 ft by 3 inches. When I cut it on the saw, I was totally surprised - it was teak colored inside. Not as dense as teak but teak colored - while the outside that had been subjected to a few years of UV was the color of rich brown walnut.
This is what his photos in the OP remind me of - brown in the original, and teak in the fresh cut. Either the 1. "lighting" differences between the first set and second set of photos created that difference in color, or 2. the difference is due to one part having been cut a few years ago and UV on the tannins in the wood caused it to change vs the fresh cuts.
QUESTION to the OP: how (method) did you arrive at the density of the wood in question? The density does pinpoint a closer approximation of the species. There are caveats to density, but it does eliminate many species while giving a narrower band of species to choose from.