No, they aren't. This is an approximation taught to you in high school to make certain problems more tractable. You've got at least two methods of generating non-spherically-expanding EM waves sitting in your pocket right now; neither your phone's screen nor its flashlight are perfectly spherical in emission. This is trivially observable by the fact that the orientation of the phone impacts your perception of its brightness.
It's true that you can't make a "fully" directional EM wave with no spread whatsoever, but you can make it arbitrarily small with engineering effort, and they're trivially not spherical.
https://en.wikipedia.org/wiki/Gaussian_beamI don't think anything from Earth will be detectable beyond more than a few light years.
https://en.m.wikipedia.org/wiki/Parabolic_antenna
I think we generally believe that the dishes are used just for receivers but they are also used in directing transmitters.
In fact, there are also heavy regulations for high-speed long distance directed microwave antennas to not spread the signal too broadly:
https://www.fcc.gov/Bureaus/Engineering_Technology/Orders/19...