The term P2W has been "pay more money than others to skip things they have to spent time doing" for well over a decade at this point. PW2 is just catchier.
MMOs are designed around time investment. If you can pay more real money than someone else in order to spend less time doing X thing, it's P2W. While other players are mindlessly farming for mats and gold, you already have them an are on to the next thing that will make your character better, or getting practice time in in PVP that the other guy isn't getting. I'm aware it should probably be P4A (pay for advantage) but we've been using the term in that way for many years.
That's not the definition I've used for it, and the way you use it is ambiguous and unclear. There are really four scenarios we want to distinguish between:
1.) Spending money is neither necessary nor sufficient for winning - this is most offline games.
2.) Spending money is sufficient but not necessary for winning - call this the Level Boost scenario, where players can pay to skip some content but not to be guaranteed victory. By my lights, this is where Lost Ark is at. The main question for games in this category is whether, and if so to what extent, the leveling process is slowed down to unfun levels to encourage people to spend.
3.) Spending money is not sufficient but is necessary for winning - The Magic: The Gathering option. You have to spend money in a multiplayer game to get to an even level with others who are playing it, but once that minimum level is reached, the playing field is even. This is not very common.
4.) Spending money is both sufficient and necessary for winning - the paradigmatic Korean MMO problem.
P2W should refer only to the last category, because otherwise you compress categories 2, 3, and 4 into the same category, when the distinction between those scenarios is really important for figuring out how the cash shop will affect your experience.
Frustratingly, I don't think I've heard anyone discuss the most important question here, which is how much Lost Ark's option 2 design leads it in a frustrating or unfun direction.