Halo is more “figuring out how to defeat this room of enemies IS the puzzle” whereas Metroid’s puzzles are platforming and figuring out how to apply this new item to the areas you’ve already visited, and there just happen to also be enemies to fight.

Visually maybe but not gameplay wise. They are very much Metroidvanias (that genre isn’t called that by chance) where you collect gear to open up the maps more and more and shoot aliens on the way.

I really loved Prime 3 on the Wii. One of the few shooters that played well on there. I got the trilogy when that was ported but got stuck somewhere in the first game. Was too proud to look up a walkthrough.