To be fair, the mirror universe in general, even in the DS9 era, is kind of Star Wars-y.
In general, though, it sometimes gets annoying when the franchises swap aesthetics, even back to V when they did bargain bin Mos Eisley (the bar in III was hilariously campy, though). Recently, I watched the first episode of a certain Star Wars series on a friend's recommendation (I wouldn't have otherwise), and at one point, I was like, "What the heck! This is supposed to be a rough pirate ship, but there's so little weathering on the set that this could be a Federation starship!"
I secretly wrote "star wars" in sharpie on the undercarriage of my 2002 hyundai elantra and would you believe it to my eye it looks no different whatsoever