For me only 1e or earlier feels "old school" when talking about D&D. But that has more to do with my subjective, personal history with the game.
It feels "old school" to me when you have that awkward but magical combination of wargame chocolate mixed into your collaborative story-telling peanut butter. The dice are not ONLY just randomizers to facilitate improvised story telling, they also serve to inject chance into math-informed tactics.
I like some "old school" elements like deadlier play, XP for GP, somewhat crunch--but greatly abstracted--tactics, looser exploration and social pillars, etc., but I can play that just fine--easier in fact, with 5e.
When I think back to how D&D was played by most people I had exposure to playing with back in the 80s, I think video games made a lot that outdated. Detailed and complex charts to resolve combat are better handled by computers.
Of course, that just opens up a different can of worms, because a lot of that complexity was brought into the game with 1e. So 1e really isn't representative of how the game was originally played. But if you take the small-group/individual-level war game crunch out of it, its not the same candy.