1493 = "doctrine of discovery" ? Not really

The pope's document from the 1500s blows me away
NYTN | 15 Sept. 2024
https://www.youtube.com/watch?v=qyxBf2FppPE

2:14 I have now perused the transscript after perusing an English translation of the Bull.

You do not appear to be citing it.

Now, the wording "terra nullius" doesn't actually appear.

If you are familiar with Lord of the Rings, the Pope doesn't ignore the existence of Indians, nor equate them to Orcs, he's more like equating them to hobbits who need some solid protection. There is a huge difference between a police officer being told by the local pastor "that hippie camp doesn't belong here, take it over and if you find some things, like fuel or cars or trinkets, taking them isn't stealing" and a Catholic priest telling the police officer "that hippie camp has some naive people, make sure they get due protection, that they don't get bothered by Hell's Angels, that they don't get exploited by the Coke mafia" (Coke as in snort, not as in famous drink from Pennsylvania).

And what the pope was saying was the latter. He did not say one word about taking over land as real estate property from the inhabitants, he was making the King of Spain police officer and judge in the areas. Not land owner.

Go and check the actual document.* And by the way, any Conquistador rhetoric from later on saying things about human sacrifice, homosexual practises, cannibalism was totally absent from the document. The inhabitants are described as:

wherein dwell very many peoples living in peace, and, as reported, going unclothed, and not eating flesh. Moreover, as your aforesaid envoys are of opinion, these very peoples living in the said islands and countries believe in one God, the Creator in heaven, and seem sufficiently disposed to embrace the Catholic faith and be trained in good morals. And it is hoped that, were they instructed, the name of the Savior, our Lord Jesus Christ, would easily be introduced into the said countries and islands. Also, on one of the chief of these aforesaid islands the said Christopher has already caused to be put together and built a fortress fairly equipped, wherein he has stationed as garrison certain Christians, companions of his, who are to make search for other remote and unknown islands and mainlands. In the islands and countries already discovered are found gold, spices, and very many other precious things of divers kinds and qualities.

Obviously, building garrisons would be involved in taking political control over an area, but taking all of the land as property for new settlers equally wouldn't.

Relations between Spaniards and Indians soured quite a lot compared to this in the time when Cortez witnessed human sacrifice in Tenochtitlan. And even so it never (as long as Spanish Kings had governors rather than ex-colonial lands had independent presidents) soured as much as it did in US in the trail of tears.

I suspect you know Spanish, so, how about reading the article** "Encomienda" in the Spanish Wikipedia?

* I don't mean the intro, I mean lower down on this page:

Inter caetera by Pope Alexander VI (May 4, 1493)
https://encyclopediavirginia.org/primary-documents/inter-caetera-by-pope-alexander-vi-may-4-1493/

** Spanish, not English, wikipedia articles vary from language to language, and this subject highest quality would be in Spanish:

https://es.wikipedia.org/wiki/Encomienda