That’s a beefy looking TKL. Very nice.
Can confirm those are Art Box switches; they have the branding on the side instead of the back / front. (Silent Box Browns are also like that, but they have a round stem and only come in the 3-pin flavor as of now.)
I’ve been doing some experimenting with Box Browns and Silent Box Browns today, and I’ve found they do take well to lubing. Hitting the rails and all the lower stem surfaces (below the “box” shape, and excluding the tactile cam) will make the switch noticably more smooth.
(Some Box housings do have dust ejection ports on the bottom, but that really shouldn’t affect lube retention at all, at least when it comes to the surfaces that matter. I’ve seen discussions about those ports where people assume that lubing a Box switch is totally pointless because the lube will just get ejected anyway - and after closely inspecting the small number of parts, I’m gonna say that’s some ol’ shenanigans.)
Like with most tactiles, lubing the cam as well will further improve the smoothness but reduce the tactile weight - however unlike most tactiles, it will also encourage the switches to lightly “click” on the tactile bump as the tiny pusher slips off the peak of the cam. (I believe this would be true of any Box tactile switch to a varying degree depending both on the cam profile and the leaf weighting.)
This could either be great or bad depending on what you want out of the switch - but hitting just the rails and springs with some lube should clear up that textured travel feel.
Edit: About the crooked cap - try sticking another cap on that switch and see if it is similarly mis-aligned. I’ve had cases where the whole switch was rotated a tiny bit, I’ve had others where the switch stem was slightly flawed and twisted (the Box switch thing), and most commonly, I’ve had twisted stems on keycaps.