First, clarification is in order: Do you mean bog-standard Autopilot or Navigate on Autopilot (NoA)? In standard Autopilot, the car should not be doing lane changes, period, even if the car is optioned with NoA or FSD. Thus, I tend to assume you mean NoA, not plain Autopilot, but this should be clarified. If I'm right and this is NoA, then what are your options for confirmation of lane changes? There are at least two values (to require driver confirmation before changing lanes and to enable the car to do so automatically; there might be a third that I'm forgetting). Your question seems to imply that no confirmation is set, but it'd be good to have this verified. I have mine set to require confirmation, and in this mode, the display will start blinking to alert me that it wants to make a lane change, and it specifies why it wants to do so -- for instance, to move into a faster lane or to "follow the route" (which is often completely bogus; it'll say it needs to be in a particular lane to "follow the route" even when there are no exits or forks for miles, so any lane will do). I've never set the option to let the car manage lane changes without my approval, so I don't know this for certain, but many other Tesla messages appear for such short periods that I can't read them. This doesn't happen with the NoA lane-change messages, since it leaves the message up until it receives a confirmation or until I cancel it. It's conceivable that in your case, the message is appearing and then disappearing before you can read it. If you see this behavior often enough, you might try setting the option to require confirmation before the car will change lanes. That might enable you to read the message. If your car, like mine, is set to require confirmation, and maybe if it isn't, then a sudden lane change like you describe is most likely caused by the car detecting a hazard and changing lanes to avoid it. You say there's no obvious cause, so if this is what's happening, it's a false alarm. The driving visualization might briefly show what appears to be a stopped car or cone or something in the lane ahead, but of course if you're driving at highway speed and attending to the road, it'd be easy to miss this clue on the display.
I've seen the second behavior you relate many times. It was quite common when I bought my car (in early 2019), but it became very uncommon in the last year or two. In the last few months, though, I've seen it reappear again, but not with the sort of maddening frequency I saw in 2019. I don't know the cause, other than that it's a bug; nor do I have a solution or workaround, except to remember that Autopilot, NoA, and FSD are all still officially beta-test features (with increasing levels of beta-ness, as it were), and so require vigilance when being used. Be prepared to intervene when (not if; when) the car does something strange or even dangerous. One caveat: I'm on the FSD beta build. AFAIK, this doesn't greatly affect the Autopilot/NoA stack, but if I'm wrong, then it's conceivable that the return of this aborted lane change behavior is unique to that build.