Native derives from the Latin nativus, itself derived from natus which means birth. This morphed into Old French natif in the 1100s, and worked its way into Middle English by the 1200s. Its earliest known definition meant innate, inborn, or natural. Examples:
So aungelik was hir natif beaute That lik a thing inmortal semed she. (~1385)
…chaungid hath vpon hir visage Hir natif colour. (~1425)
There was a similar meaning of an attribute belonging to someone by virtue of their birthplace. The phrases native tongue and native language are still common today:
Of commyxtioun dyuers..they hane corrupte her first natif toungis and usyn now Ine wot what straunge..blaberynge & cheterynge. (a1447)
And I conuersaunte and borne in the partes, where my natyf langage is moost corrupt. (1480)
Another early definition meant born in servitude:
Gif thi natiff man or thi bonde haf fylit thi land with guld. (~1425)
Of bondis natif & fugitif clamand to fredom..quhen ony askis ane other in bondagis as his natif bond. (~1455)
This meaning is completely obsolete.
By the 1400s the meaning of born in is also attested:
Purposyng to gon a-geyn in-to her owyn natyf lond, it was telde hem þat þer wer many theuys be þe wey. (a1438)
When the first English-only alphabetical dictionaries were written, this was one of the primary definitions.
natiue, where one was borne, or naturall. (A Table Alphabeticall, 1604)
Natiue. Naturall: That place where one was borne. (An English Expositor, 1616)
The meaning of indigenous to was a straightforward extension.
My ancient natife kingdome. (1630)
This usage is captured as original; natural in Johnson’s famous dictionary in 1755.

Johnson took 7 years to write the most thorough English dictionary ever written at the time. Through the power of the internet, he will now be remembered as the guy from that one meme.
Native also developed as a noun, meaning either someone born in or someone indigenous to. Within my own lifetime, some saw it as a pejorative due to association with the language of colonizers. For example, this commentary:
The evil of colonialism is not oppression but contempt. Eminent Victorians despised their own lower classes and certainly the Irish… as much as they did any other people they called natives. (1985)
Now, native to mean indigenous and a native to mean an indigenous person seem to be preferred terms in most(?) circumstances. Corpus results of modern text have endless examples of both usages.
The born in usage is still common, though, and is usually in reference to a city or a state. People know that this usage doesn’t indicate membership in a Native American tribe because of linguistic patterns. The phrases a [city] native, a native [city/state demonym], etc. are simply not used to describe Native Americans as such.
(Which makes sense. Hardly any species, tribe, or any other group is indigenous to a single city.)
…Texas native Jonny Coyle of the Rattle Snakes recently completed a court ordered stay… (2019)
He has lived two years with our neighbors, the Kinnersleys, and is a native of Lawton. (2019)
Whether you're a Las Vegas native, local, or visitor, we have fun for everyone and celebrate and uplift EVERY BODY! (lasvegaspride.org, accessed 11/8/2023)
When the N is capitalized (and not the first word of a sentence), then the word is always shorthand for Native American or another indigenous group.
This accounts for how Native values and instincts were present in the crucible of rock… (pbs.org, 2019)
To say I’m a native Chicagoan is different from saying I’m a Native Chicagoan. If you were not a Native American and wrote the latter, people would be rightfully offended. Be careful typing on your phones.