Has anyone used this PCP for Silhouette Air? It's still kind of new and I have not shot one of these yet.

We have never had one at a silo match however I did look it up and check the specs. I suspect that we would not allow it because it is too powerful and would damage the targets. We have extra thick steel targets too but I still would expect target damage.
I would also generally note, I say generally!, that these super high velocity air rifles are usually not as accurate as the slower less powerful ones.
On a very personal note, that thing is really ugly!

Are the Air Rifle matches usually .177 caliber?

It's not legal because it'll damage targets.

Dustin

Yes, most shooters at our matches shoot .177 cal. rifles however .20 and .22 are legal if they do not damage targets. I am not sure if .25 cal. is legal. I would have to check the rules. Rule 3.3 says nothing about caliber, but again they cannot damage the targets.
Most shooters stay with .177 because of the flatter trajectory in silhouette, also in field target but hunting is a different game altogether.

What is the typical muzzle velocity for Silhouette Air?

Don't focus on velocity. The pellet has to hit the animal and have enough energy to knock it off the stand. Accuracy is more important than power. The exact same thing is true in HP silo where shooters don't want any more power than they need to knock the animals down except there they are simply trying to shed recoil.
There is no specific velocity in airgun silo. Velocity depends on pellet weight and power of the rifle. Both can vary depending on what you shoot. A 10 meter gun shoots at around 6fp of energy while others shoot perhaps up to 20 fp of energy. Lots of airguns are more powerful, but again, the power is not needed, does not translate into more accuracy, and probably will damage targets.