This is the shortest of the many possible ascents to Mulhacén, with one other southerly start point from Trevélez joining this route (after a VK!) and the route from Capileira taking a parallel tougher path via Refugio Poqueira.
There is already a Strava segment for this ascent - https://www.strava.com/segments/12928340. Note that the official FKT route sticks to the trails where available (there are other routes relying more heavily on the gravel fire road, which you may wish to consider on your descent).
The terrain varies from narrow woodland trails to gravel paths to the traditional steep/rocky ascents of this area. You will find gradients of 15-35% in the rock path up to Mulhacén II, though there are surprisingly many "runnable" sections before and after that.
In terms of supplies, I have done the route in Unsupported style, packing 3x500ml liquids in my running pack as i might do for any longer run. Note in the Sierra Nevada mountains, there is no potable water available along the way. Unusually, i did not cross any mountain streams either (on 30 Aug) - in most months you would expect to see streams from the snowmelt above, which you could drink from through a filter.
You can be up and down the route in a relatively short time, but do provision yourself for the total trip time, as the drive up to the start point at Hoya del Portillo is slow and winding, finishing with a long gravel path that will leave your car quite filthy :-)