I am wondering if paying real-world money will give the player an in-game advantage, or if the microtransactions will be purely cosmetic, or maybe something similar to what Team Fortress 2 does where everything is equal but different?
Hmm, now that depends on what you see as p2w. They will likely do a DBD-like thing where content like traps, suits, weapons, guards, and hardware are locked behind DLCs. It technically is p2w, as it can give an advantage depending on how strong those things will be. But for now, with only speculation, it is hard to say if it will or will not be p2w.
If you don't like a strategy being used by a base then just leave. Even if there are additional traps or suits unlocked in the future as DLC the base game right now is good enough to get kills and prestige. If you want to play without additional content then you don't need to purchase it. But for myself, I would like to pay for additional content because I want there to be an incentive for the developers to make additional content.
Worth noting that some of the UI in the open beta heavily implied the existence of trap-, block "class"-, and guard-type limits. For instance, while the open beta had 8 or so traps, the limit was the same number (8 unique trap types). This will severely limit how P2W they can make the game - if they add 20 new trap types that are all overpowered in some circumstances, bases won't be able to jam all of them in, only a subset.
That's not to say they couldn't add an overpowered DLC trap; just that there's going to be limits on how much damage that can do, especially if they stay on top of balancing. I've not played DBD so I don't have much context for how well their balance team handles balancing DLC vs existing content; other people can speculate on that far better than I can.
All the traps/guards/etc have been said that you can unlock through playing. So buying the DLCs gives you access to the thing RIGHT NOW without grind.