There's always a sort of buy in depending on which format you play, but once you've spent a bit of money on some cards it's usually more skill in deck building and playing than money spent.
Personally, I play mostly Modern in a casual way, but even when people bring competitive magic decks and we swap decks the same players usually win.
"Once you've spent a bit of money on some cards" means I can be the greatest player of all time, but if I haven't paid for the cards, I can't win. They don't just give you these cards for being good. You can't find them scattered around the environment. You have to buy them, somehow.
What is pay to win in your mind? The phrase generally means "no matter how good you are, if you are unable to buy a certain set of cards you can't truly compete in the meta". There are more or less expensive decks, but typically the cheapest of the best decks in any format cost $50+
Edit- This is for constructed formats. Obviously sealed is more of a pure skill, low cost format.
However, "pay to win" is generally understood to mean that there are significant marginal returns to spending thousands of dollars past the entry price paid by the typical player. This isn't really true of Magic: the Gathering.
"Pay-to-win" is one of those weasel phrases that doesn't really mean anything specifically.
What is a game that represents "pay-to-win" in your mind? I think the definition you're using might be "generally understood" but it also might be generally understood that "pay-to-win" means "high[1] cost of entry"
[1]-high cost is relative to each person. could be 10 bucks, could be $1,000
If Magic =/= pay-to-win then neither do those 2 specific examples you just gave.
I don't believe there is a competitive (read: >2 players) game that is "pay-to-win" if you feel that magic isn't pay-to-win
Yes, in some sense the difference between M:tG's "~$50-500 for the best game pieces, or to enter major Limited tourneys where everyone is forced to start from scratch, for a year; only skill matters from there" and Clash Royale's "~$5000, or an amount of time and attention worth >$5000, for the best game pieces, otherwise you're strictly behind someone with higher-level versions of your pieces" is only one of degree. But again, a far larger fraction of M:tG games involve both players playing with what they consider the best pieces. I don't believe I'm the only one who sees this as amounting in practice to a difference in kind.
I can't answer your question because I tend to stay far away from "collectible" games.
But, if 13-year-old you scrapes together your lunch money and buys a "Magic: The Gathering Spellslinger Starter Kit Core Set 2020" (https://www.amazon.com/Magic-Gathering-Spellslinger-Starter-...), are they going to be routinely beaten by someone who spends $100 on booster packs? Assuming roughly similar skill levels, that is?
Yes, you need cards to play, but in my mind pay to win means the amount you've spent outweighs your skill at the game. There are plenty of games like that, and I'd argue Magic isn't one. You can do really well in Magic with a cheap deck and I have seen plenty of people lose hard after buying the most expensive popular deck that they didn't know how to play.