Older Star Trek, as Roddenberry saw it, more closely followed your desired formula. I mirror your sentiment, I love that Trek at its best is about culture, society, people, etc. Unfortunately war is a comfortable crutch for shows like Star Trek, I’d be surprised if anyone could make a sci-fi TV show entirely without it. Personally I’ll take entire seasons of filler about things like fungus people or Law In Space.
Up to a certain point Trek managed to keep military conflict at bay, to a degree. There were episodes about the Neutral Zone, or a Klingon raid, or what have you, but the plot eventually would cycle back to other matters. It’s DS9 where the show runners intentionally dove into those elements, and to their credit the show found good conflict there. How do you feel about Voyager? I prefer it to DS9, despite thinking DS9 is a stronger show and preferring the cast, because it focuses more on the things I like in Trek while DS9 at its root is about war.