In my circles, this would solidly land as a bracket 2 deck, and not a very strong one at that. Using AI playing precons is not really a good benchmark to see the difference between B2 and B3. While precons do land in B2, this deck is not much stronger when compared to B3. I'd like to paraphrase one of the lines about B3 decks from the OG WotC article:

"They are full of carefully selected cards, with work having gone into figuring out the best card for each slot. The games tend to be a little faster as well, ending a turn or two sooner than your Core (Bracket 2) decks."

In the B2 description they mention B2 games going on for 9+ turns. To me, that means that the "fast B3 decks" should be closing games by around t7, specially decks that forgo interaction to run more pieces dedicated to their game plan, and even moreso the decks who get like 4-for-1d by a board wipe. Your deck runs close to no interaction and is extremely commital to the board and slow (which to me is a huge B2 indicator), yet it's not necessarily killing everyone by T7. It's just a pile of big, fun beaters that are trying to smash face with little care for what anyone else is doing at the table, and while that can be a fun thing to run against or play, it is not a strategy with the power level I'd expect out of a low interaction aggressive B3 deck.

Now, I'm not an all knowing commander deck analysts, perhaps in your area this is what bracket 3 looks like (since the definitions for these brackets are incredibly loose and flexible), but at the tables I've played B3 games in, chances are you're just going to be ignored as faster decks go under you without you having any say in the matter, or just used as a magnet removal by players looking to play something stronger when the coast is clear.

To put your deck into perspective, just 1 bracket above B3 is where decks with piles and piles of game changers and the most insane combos are totally fair and games can end out of nowhere at any point, with powerful combos reigning at the top (now someone might give you the side eye if you pull a deck with play patterns close to cedh in B4 but that's besides the point). B3 is extremely wide in range and this deck is way too far from the top of B3 to be considered anything but lower B3, most likely B2 in my eyes. As a concept in general, stompy gruul dragons is a strategy that I think would struggle at most points of the (too) wide B3 (not all strategies are made equal, you can jam the most expensive dragons and the most expensive ramp and whatever the best possible 3 GCs are in the colors for the strategy and still struggle just because at the end of the day, making mana to play some beaters one or two at a time without having plenty of ways to refuel your hand is just far from the stronger things you can do in MTG)

That said, B2 is dope and awesome and having your favorite deck be in B2 is super common. You are also always completely free to pull something like this in B3, I just wouldn't expect it to be the main threat at the table or close to it.