This all assumes that all life in the universe is governed by nucleotide RNA sequences (which there are strong arguments for that I won't shit up the thread with) and they can locate another life bearing world (which we are getting pretty close to that in the modern world). But if we want to treat this as completely grounded in science, the food logistics problem is real. Even a hiccup in supply will result in a ton of starvation, so they are likely going to do some sort of big draw down to whatever they need to physically build Hive Radio 2.0 and sustain themselves. That is unless they really just want to send a "come pick up resources" signal back home, which seems more likely.
Also bear in mind that any transmitter would likely have to be in orbit with something resembling a geostatic rotation. It makes no sense to try and overcome the atmospheric and magnetospheric interference, for one. And if you put the thing on the surface even with sufficient power, you won't get a signal out to a target except for the millisecond window where your planetary rotation aligns with the target especially given the fact that the target itself is moving in an orbit of its own constantly. If you are talking something omnidirectional with the kind of range they are talking about, then we are into post Star Trek power sources and transmitter materials made of unobtainium that don't immediately melt the moment you pump that much power through them. And you are also still talking a space based transmitter because trying to sent a signal through the planet core is not going to fly and pushing one out of that intensity will potentially fry life in the general vicinity and certainly knock a nice big hole in the planetary magnetic field. Remember they specifically used radio, probably because its a signal less advanced civilizations would have access and monitor. Especially the kind of retarded civilizations that recreate alien RNA sequences from outer space in relatively unsecure labs near major population centers instead of an Antarctic base they can nuke if anything goes sideways, which is probably the most scientific plausible thing about the show (our stupidity).
So yeah, don't try to treat this show like it is hard science based. Its a psych study of an angry suburban Karen box muncher with a sci-fi backdrop. On that basis, its actually pretty good.