Interesting question. Kinda depends on what part of the series you’re referring to tho. The first game was a lot darker and grittier in general, so prolly more dystopian and post-apocalyptic, along the lines of Mad Max. Each game afterward has gone progressively more sci-fi and silly, with 2 being a compelling balance of grit and humor, and 3 being, as they like to call it, total mayhem.
Space cowboy is definitely a good descriptor in general, but a lot of the dlc’s veer off into their own realm. For instance, Zombie Island in 1 is kinda like an old horror movie, Dragon Keep in 2 is high fantasy, and the Handsome Jackpot in 3 is like an 80s heist thing. And 3 in general feels more like a silly sci-fi epic along the lines of Space Balls. But yeah, space western is prolly the best way of summarizing it. Like Cowboy Bebop, Firefly, or maybe Mandalorian (I haven’t watched it, so not sure).
Personally, I prefer the aesthetic of 1, but I know I’m probably in the minority on that