Real people are inseparable from their culture.
But how many cultures does the Klingon Empire hold?
If you were to imagine a Empire that had a population of Klingons numbering in the multiple tens of billions, would there be any real expectation that they would all be of the same ethnicity?
Add to that all the non-Klingons species in the Empire.
but modern Klingons are unbelievable. There is no convincing way to rationalize the continued existence, much less progress of such a society.
Because of the nature of the show, we see mostly (not exclusively) the warriors and the leaders of the Empire. Just as we see mostly Starfleet activities when it comes to the Federation. The warriors are likely a tiny percentage of the total Klingons in existence. America has a large military, but the active duty numbers are only 0.45 percent of the total American population. The majority of the Klingon population could go extended periods with no interaction with a warrior of any kind. I can't remember any mention that Klingon warriors "police" the general Klingon population.
The warriors exist in a societal pocket.
The bulk of the Klingon population goes merrily about the daily affairs of the Empire. Engineers, designers, and programmers increase the technology over time. The warriors do not generate the technological advances, and they don't impede it, they utilize it as it arrives.
Modern Klingons are stupid.
Except they're not. Stupid people don't accomplish what the Klingon are shown to have accomplished. Stupid imbecilic fools don't solve problems, efficiently operate starships, build (or conquer) a Empire, and hang on to it for multiple centuries.
Kirk: "And unfortunately, though the Klingons are brutal and aggressive, they are most efficient