Nothing you say there is incompatible with what hard science fiction is. As I've already explained, it's a profound misunderstanding of hard SF to think that it has to center on explaining the technology or lack a focus on character or theme. That may have been generally true in the 1950s or '60s, but it's an assumption that's a generation or two out of date.
The only thing required for something to be hard SF is that its science is founded in reality and credibly extrapolated from it. And that's exactly the founding spirit of Star Trek. Roddenberry was tired of the fanciful children's shows that dominated SFTV and wanted to prove that SF could be as serious, grounded, and believable as any adult police procedural or medical drama or Western. He urged his authors to make sure the characters were written believably and behaved authentically regardless of the futuristic setting, and he consulted with scientists and engineers in an effort to build a more credible future environment than the handwaved nonsense of the rest of SFTV. Both of those, the character realism and the technical realism, are rooted in the same spirit, the desire to build on believable, naturalistic foundations. It's absurd to think they have to be at odds.
I often like to cite a column that Stanley Schmidt, the longtime Analog editor who mentored me and started my professional career, once wrote. He argued that it's a fallacy to think SF writers have to choose between a focus on characters and a focus on setting, because the two are integral to each other. The setting informs the characters, shaping their options and worldviews, defining their opportunities and limits. Characters act and react in response to their environment as much as they do to other characters. Thus, the setting is essentially a character in itself, and deserves to be approached with the same care and authenticity as the other characters are.
