Nothing to do with Spanish settlement. Other than St. Augustine, none of the Spanish settlements are even inhabited anymore. Florida had 2.7 million residents in 1950, barely more than Iowa. The population is now over 20 million.
There are - unsurprisingly - a number of factors for this. It’s mostly due to the Cold War, which made Florida important as:
-a naval staging area
-the closest state to many potential future communist countries
-the home of the space program
-the place where most Cuban refugees washed up after the revolution
-a base of operations for Gulf oil production
And so forth. The space program had a knock-on effect in that it made Florida an attractive place for aeronautical research and development generally, so Lockheed, Boeing, Hughes, Raytheon and other space contractors built plants and offices here for non-space stuff.
Then there’s Walt Disney World, which turned Orlando from a backwater into a thriving tourist destination (especially after Universal, Seaworld, and other parks followed).
All of this happened between 1954 and 1970 or so. Before that, most Florida jobs were in agriculture. Since then, most of our jobs have been in tech and tourism, though we still have a lot of labor-intensive agriculture like orange growing.
It didn’t hurt that home air conditioning became affordable after 1950, which made Florida more livable (particularly to Northeastern retirees…) Having enough people also made it worthwhile for the federal government to start filling in swamps, creating space for golf courses and yet more theme parks.
Tourism allows the state government to function without an income tax, which makes the state attractive to business and people (though it brings its own issues like terrible schools).
Of all the densely populated states, Florida is somewhat unusual in that it doesn’t have a true center of gravity. Rather than having one megacity and a bunch of smaller cities, we have four major cities - Jacksonville, Tampa, Miami, Orlando - without having one dominant one (Miami is dominant if you count by metropolitan statistical areas, as the Miami metro area includes Ft. Lauderdale and the Palm Beaches).