How long does it take living at altitude to fully adapt?

I recently moved from about sea level to about 5000 feet (1500 meters). I’ve read VO₂ max goes down something like 2% or 3% for every 1000 feet of elevation gain, and my personal experience seems to bear that out: I can see the effects on power numbers on climbs and the trainer.

I’ve also read it takes about 3 days to acclimatize to altitude, but I’m not entirely sure what that means, objectively. I get the impression it means one should arrive at altitude 3 days prior to a big effort to avoid the more acute symptoms of altitude sickness, like headaches and passing out.

But I’m not sure it means within 3 days one’s performance will be back to what it was.

If one is permanently moving to a higher altitude, is there some longer time after which the body will physiologically adapt to the reduced oxygen, and performance will return to "normal" levels? And if so, approximately how long is this adaptation period, and is it affected by training or is it more a function of simply living at altitude?