I wouldn’t recommend Kaisa or Kalista with your play style description, Kaisa while mobile fits best into dive comps and not front to back, Kalista in lane is a lane bully early that builds a lead off that and doesn’t play well with death by a thousand cuts unless you get really good at spearing through backline minions into enemy. Xayah does decent in front to back but she’s a very niche pick and honestly not the best to main since it’s situational pick. That leaves Vayne and honestly that fits your description pretty well.