I'll look more into the history of this chunk of the US, sounds interesting. Funny how the US has so many distinct origins but now it's so vastly English-speaking and Protestant besides first generations immigrants.
Due to acquiring the SW and having Mexico on the border, there is a major Spanish/Hispanic impact on the US culture. It must be the most common second language in the US and in US schools. Americans learning Spanish is probably comparable to East Europeans learning English in the 1990's. Me, my mother, and brother all learned it, and he and I sometimes talked it as a kind of little secret language between us when we want to talk in code.
Los Angeles' population in 1840 was 3,330. Santa Fe was the capitol of New Mexico and in 1850 its population was 4,846.
That sounds very tiny, right? That's by today's standards.
Back in 1850, the capitol of what was to become the Confederacy, Richmond VA, had 27,570 people.
So Santa Fe was like a small city in those days. Nowadays, it would be only like a regular town.
Nowadays LA is one of the largest cities in the US with 4 million people. L.A. has a TON of hispanic culture. Some of that is from recent hispanic immigration in the last 50 years.
The US is practically all English speaking because it needed a common language to work successfully. The first and second generation people in the immigrant cultures wanted very much to learn English instead of speaking Polish, Irish, or Italian. It was kind of a no brainer for them and their children.
The US is probably 50-70% Protestant in heritage too, because it has lots of English, Scots, Dutch, and Germans. The rest is usually Catholic.
The basic origin is a set of English colonies. After independence they took over the Spanish, Russian, and French colonies in today's territory of the US, but those did not have much settlement population, you are right. Those areas were "vastly uninhabited" by other Euros compared to today.