I like the distinction you've made here. Star Trek, much as I love it, posits lots of highly unlikely stuff like transporters and warp drive. By the time we can command molecules, time, energy, and space to the extent Starfleet demands, we won't even need to travel: We'll simply assemble new Earths right in our own solar system, perhaps drawing off the required mass from the sun and transmuting it to heavy elements via the nuclear fusion already known to exist....I'd say that "hard science fiction" is a better description for the mission in this movie because of its adherence to what we know of real world concepts. The works of Jules Verne, H.G. Wells and even Star Trek seem to be closer to "soft science fiction"...
But science fiction is aspirational: I consider Stanley Kubrick's 2001: A Space Odyssey (1968) the ultimate "hard" movie. Still it indulged that fantastic quasi-metaphysical sequence near its end by way of defining a meaning for our existence.