Its like, these guys have literally saved the Federation a dozen times over, decorated heroes of the Federation, famous bridge officers on the Enterprise, and one guy is being rude to admiral Kirk, and the other is calling a guy tiny for just making a joke.
How many people would you recognize from Seal Team Six?
This is one of those situations where people (like the creators of
Lower Decks) forget that in-universe characters are
not the audience. There are no "famous bridge officers." Dr. McCoy is famous in the medical community, but something tells me these cops haven't read any of his papers on comparative xenobiology or adaptational retroviral pathology. They don't have access to the (mostly still-classified) official logs of the
Enterprise's five year mission, and probably wouldn't care if they did; they have
jobs of their own to do.
These aren't eager young Academy students nerding out over their career heroes, or well-travelled starship officers or diplomats; they're
cops who've probably never even left Earth except for a three-day vacation to Risa.
The guards may have seen news footage of Admiral Kirk after the V'Ger Incident (which would be the only "saved the Federation" event they'd know about), and they may have been told that their prisoner served with Kirk back when he was a captain, but they have no way of knowing that the short Asian guy is part of Kirk's crew; they think he's just some message-runner from Starfleet Command here to summon the Admiral.