In strict, it very closely keeps in the middle of the lane. That's not how I normally drives, so it feels scary. I usually bias away from oncoming traffic. It's probably fine on a wide highway, so this is more about me not feeling in control.
However, in relaxed mode, it seems to have the issue you're describing where there's too much slack, and it looks like it's playing pong between the lane dividers. Have the exact same worry about what this looks like to others...
I've only ridden in Teslas, not driven one, but it seems like it's probably got the best following/lane-keep system on the market, although the last time I rode in one -- admittedly about two years ago -- it was markedly jankier when the driver engaged more "self-driving" features, e.g., have it change lanes, take exits based on its own GPS guidance, etc. It was impressive that it could do it, to be sure, but it was the self-driving version of your reckless friend in high school you do your best never to ride with.