For a mid-UHF fractal antenna, what kind of power can be used to
transmit, 100 watts, 1000 watts, 10,000 watts...?


I've had such antennas at very high QRO, but not for ham use.

Some designs, as with antennas in general, will arc at very high voltages.
Others will not.

It takes experience to pick the design that deals with the specs, including a
HV spec.

That's a commercial issue and beyond the scope of this NG.

73,
Chip N1IR