You didn't find them in Halo 2 because Bungie had tools to remove unused data in both Halo 2 and 3. But yes, Halo 3 is basically Halo 2's third act they had to chop off. Of course it wasn't DONE (because they would have shipped it), but it was prototyped.
Floodgate and Cortana in Halo 3 were essentially fully modeled in Halo 2.
.. we only know this because Bungie writes postmortems a couple of years later, where they said the level was too big and it was cut into two pieces - the "intro" version in Floodgate and the rest became Cortana.
The reason you can find "future" geometry in Destiny is because Bungie has always made geometry first before any encounters are placed. They had to cut an entire, geometry complete level that never appeared again because they ran out of time to place the encounters in Halo 2. In the current mode of development, it's easier to just leave in-progress content in the build than rip it out.
Heck, a couple of the supposedly 'dlc on disc' locations were thrown out and replaced in the actual patch that let us go to those locations (like the Terminus on Venus).