Most of the technology in Away is just a small extrapolation of today's technology. For example, they are still using chemical rockets instead of e.g. nuclear ones. They still use bulky uncomfortable hard-shell space suits instead of mechanical counter pressure suits.
In the pilot, it is mentioned that the lunar base is melting water from the lunar pole to pump into the spacecraft for radiation shielding, so they don't even have "magic" shielding a la Andrew Weir's The Martian.
There is no artificial gravity, no AI running the ship, no ubiquitous robots.
In almost all aspects, their technology is only slightly more advanced than ours, in some aspects, it even feels like a step backwards. (E.g. we do have experimental robots on the ISS.)
There is one exception, though: they obviously have faster-than-light communication, which is not "just" a huge leap forward from our current technologies, but in fact physically and mathematically impossible based on our current understanding of the universe.
However, I do not remember any explanation as to how this is achieved. (Unlike e.g. the radiation shielding, which the writers felt important enough to explain that they put it in the pilot episode.)
Is any explanation given about how they achieve faster-than-light communication?