For highest voltage per device you'll have to look into "vacuum state transistors" (ie, tubes) like Thyratrons, or even not-so-vacuum-filled valves like the Mercury Arc Rectifier, which is basically a thyristor. Voltage is somewhat unlimited since it depends on the length of the arc tube.
At high voltage, you will find mostly thyristors and diodes, because the main application is switching and rectifying. An actual amplifier would require something like transistors, or triode/pentode tubes, but few are actually interested in 300kV output amplifiers...
What determines breakdown voltage is the length or thickness of the insulator, so for transistors this is limited to what is possible to manufacture and of course to what customers will buy. The whole point of semiconductors is that they're tiny so you can manufacture a lot of them cheaply on a wafer, but this results in insulation/creepage distances that are not compatible with hundreds of kV.
Theoretically it should be possible to build almost unlimited voltage triodes for that juicy Class-A sound. After all it's a glass tube, you can make it one meter long for the extra insulation distance. But that would be "special order".