What does a RF wave carry?
An RF wave propagating through free space consists of a magnetic field 'waving' sideways, and an electric field 'waving' sideways at right angles to the magnetic field, both waving at right angles to the direction of travel, described as a single electromagnetic wave. You may sometimes hear the description TEM wave, which stands for Transverse Electric Magnetic.

When this wave hits an antenna, it can induce an AC voltage in it, which can cause an AC current to flow in a load connected to it.

There's no need to do ones head in with exactly what is waving, or how it 'becomes' photons when that's a more appropriate description. If you think you understand, then you probably don't, and neither do physicists whose day job is to figure out that sort of thing. I just accept I don't understand, and use whichever description is most appropriate to the measurement situation.

A reference way to measure the energy of the wave, crude though it may seem, is to absorb it in a load, and measure the temperature rise. In the case of visible light, absorbing by a black surface or better still a black body cavity would be appropriate. In the case of a radio wave, you would absorb it in a resistor connected to an antenna. A measurement absorber is called a bolometer.

Using a bolometer is not usually the most convenient way to measure the power of a wave, which is why we use photodiodes and voltmeters and suchlike. However, it is the reference way, which is the way all the more convenient techniques must be calibrated back to.