Less friction = less kinetic energy lost by the ball during the bounce = faster surface. Grass tends to be faster because grass as a surface is slick. However, the ball also bounces lower because the surface is softer than hard court.
Speed of Tennis Courts
Clay is slow not because of friction but because the clay absorbs a lot of the kinetic energy of the ball on the bounce. Clay consists of granules that can move freely. Imagine dropping a tennis ball into the sand. The velocity of the ball is reduced to zero after hitting the sand. The reason is the sand has absorbed all of the kinetic energy. However, clay actually causes the ball to bounce pretty high because the clay is spread quite thin (millimeters IIRC) and under that is a relatively hard surface of rocks. When the ball impacts the layer of clay, it craters. So the ball will be pushed upwards a little bit by the front of the crater, almost like the ball is going off a ramp.
Hard courts vary but generally, more friction = slower ball = higher bounce. Increasing the “grit” of the court would, therefore, slow the surface down. Also, the more arid the climate is, the dryer the surface will be. Therefore the slower it’ll play (wet = slick). This is why I suspect people say Indian Wells (which is pretty much in a desert) plays a lot slower than Miami, where it is quite humid. I once played on a hybrid court inside a gym that had a surface of hardwood. Almost no bounce and the ball skidded like crazy and was very fast because polished wood has almost no friction.
Tennis Courts are made “faster” or “slower by changing the composition of the surface. On grass, they change the blend of grasses they use. On clay, they add a more top layer and change moisture content. For the hard court, they add more sand into the paint that they coat the surface with, which increases the friction of the court. For all of these, they can also change the subsurface as well.