I disagree. If all land is private, you have no right to immigrate at all. You can’t travel across land that you don’t own without consent.
Of course you’ve got a “right” to immigrate: buy some fucking land.
That should be the only criteria that defines “immigration”, either in an AnCap society or what we have now: if you can pay for a freaking house to live in, then you can live in it.
“Immigration” will be self-limiting because over-immigration will drive up prices and thus reduce the number that can afford to go there.
If you mean you don’t have a “right” to walk on everyone’s land, well, sure, because if you did, there’d be no such thing as property.
Unused land should be free for anyone to move through.
“Used” is a statement about value, and since value is subjective, there can be no objective definition of “used”, so this statement just doesn’t work.
OTOH, in general, the market is going to make it relatively cheap to “move through” land whose value to the owner would not be very affected by that movement, e.g. either they won’t prevent it because it is too expensive to do so, or there will be a cheap fee for it. I think you have in mind a model wwhere all land is owned and no one ever lets someone cross their land, so everyone is stuck in their little property (and those without property have nowhere to even stand). I just think your prediction that this is how things would work out is way off, as shown by countless data points from the past and present.
I personally find discussions that assume “rights” become hopelessly muddled, unless those “rights” are explicit clauses granted in bilateral contracts. Otherwise ‘rights’ are just religion, either explicitly - some higher power, god, government, etc handed them out - or implicitly, e.g. they are “natural” and were just floating in the ether until someone discovered them.