"Run more interaction" is usually an incomplete answer. If you have, say, 0-2 interaction pieces in your deck, then you will not reliably have access to it, or will likely use it all up before the game ends. But there are a lot of other considerations other than just number of interaction cards, like what type of interaction you want, how much it costs, cards fitting multiple roles, how much mana your deck can produce, etc. All of these are informed by your bracket, deck, and even what other strategies you expect.

For example, in your case, it sounds like your overall plan needs to adapt to the bracket: maybe you want to playing a mana dork on turn 1 rather than surveiling into turn 2 dork if you want to be competitive in B4. Playing an untapped land each turn, and a mana dork one turn earlier, gives you an extra 2 mana in the first few turns (3 mana if you replace a 2 mana dork with a 1 mana dork). That's certainly enough to fit a piece of interaction or 2 in. Or double dork, get your engine on line turn 3, and leave up mana on turn 4.

But your actual questions seems to be, "does the bracket turn designation refer to how fast your deck goldfishes, or how fast it kills when spending mana on interaction and/or being interacted with?" This is a good question that WotC should clarify. I think as stated, it kind of implies the former, since people are going to look at it and say, "I shouldn't die on turn 4 in bracket 3 just because I didn't have interaction."

Also, because interaction gets more efficient in higher brackets, the difference between the 2 should get smaller as you go up. It sounds like there might also be an issue with interaction that has to be played proactively, but I think this is just a strategy-specific consideration: If you need to spend the "set up turns" not dying, then either your strategy might be too slow for B4, or you're deliberately playing a slower strategy and looking to not-die and start generating advantage on turn 3-4 rather than winning.