Power usage isn't necessarily huge. I worked on a SAR satellite a few years ago with a total RF power of <1kW.

It's pulsed as well - you send an RF "chirp" at a sub-1kHz pulse frequency. Depending on imaging mode the average power draw is probably in the 500W-1kW range.

That had a much larger resolution (6m rather than 50cm), but the resolution is a function of frequency and antenna design as much as power.

The SAR concept essentially creates an image by sending out a known RF chirp and then, for each pixel of the image, correlating the response with the expected signal from that pixel. That correlation means that even if the received signal is below the noise floor you can create an image.