The wings of subsonic planes have usually a very low surface area and aspect ratio as big as possible. However, in supersonic aircraft, wings with more wetted area (e.g delta wings) are used. Is this because skin friction decreases with speed or because in supersonic flight this type of drag is no longer the main concern?
Your question is about friction drag while the text is mainly about aspect ratio. You seem to explain the choice of aspect ratio to be based on friction drag. This is not correct.
Here and here are some good answers to explain the choice of aspect ratio. You will see that it has mostly to do with structural strength and wing volume to pack enough fuel. For supersonic aircraft the delta wing provides a highly swept leading edge, a stiff, light wing and good low-speed characteristics even with the thin airfoils which are helpful in supersonic flight.
Generally, aspect ratio becomes less important the faster the aircraft flies, because it has more air flowing past per unit of time for creating lift. At supersonic speed some of the drag is proportional to the local inclination of the surface, so the designers try to make the aircraft as sleek as possible. To put it bluntly, a subsonic aircraft likes to be as wide as possible to reduce induced drag, while a supersonic aircraft likes being longer to reduce wave drag.
Friction drag will go up with the square of velocity if all other parameters are constant. Since a higher velocity increases the Reynolds number (the ratio of inertial to viscous forces), in the real world the increase is slightly less than with the square of velocity. Since lift also goes up with velocity squared, the airplane can fly at higher altitude where the density is lower, which reduces both lift and drag.
Now you need to consider the change in temperature over altitude: Air gets cooler when it expands, and cooler air causes higher viscous forces. By flying higher, the Reynolds number goes down again and the viscous drag goes up. In total, flying faster and higher will result in a slight increase of the absolute friction drag at the same lift.
If you plot the drag coefficient over flow path length you will find that lengthening the flow path will generally increase drag less than proportionally. Only when the boundary layer is laminar and lengthening the flow path adds a turbulent transition will you find that friction drag briefly goes up more than proportionally. Sometimes it is helpful to force that transition, but mostly it comes sooner than the engineers like.
Please follow the links and read the linked answers, only then is this answer complete.