Nope, it doesn't include the Evo sidequests, and there's some other stuff Evo has with the Kai versions missing for whatever reason, like animated portraits and better graphical effects... sure what I mentioned is graphics stuff but the animated portraits are really nice imo for example. Don't get why the Kai versions don't include them, it's an odd thing to leave out considering they went through all the trouble to include voice acting lol
Apparently Kai has some straight up missing textures that still didn't get fixed for some reason... hopefully the official localization fixes it (I don't know if the fan patch fixes it since I haven't played much of it).
I also prefer playing it on my Vita anyways since I use my Switch 90% of the time in handheld mode and Zero/Azure's textboxes look WAY too small there but that's just a me thing I think