Soil cement pathways are a thing, they did it at my college at least into the 90’s. They would till in Portland and lime chips, level and crown it, then pack it and top with a thin layer of lime chips. It basically acted like a dirt path that didn’t get muddy. Tiller, drop spreader, sprayer (for water), and a sod roller. All standard landscape tools, done by the regular maintenance crew, and could do it extremely quickly.
They probably switched to concrete for handicap access, but it was an easy cheap solution.
For your situation, I would do the same thing but skip the Portland. The key is to get the slope right to direct the water to where you want it. You can funnel a portion to the tree, leave the drip line mostly permeable, and make sure to not puddle.