I keep seeing this and it kinda confuses me, because the only thing in the game that feels like Halo 3 to me (beyond an art style that's a little closer to it, but imo doesn't hold a candle to it if I'm honest), is the return of equipment. That's a significant thing for sure, mind you... but am I missing something else? I say this as someone who holds Halo 3 near and dear to his heart. And I think this game is very fun, but it feels closer to Halo 5 than 3 to me by a significant margin, gameplay-wise.
I felt like you did when I initially played. But now that I have about 6-8 hours on the game, I'm feeling more old Halo vibes than Halo 5 vibes.