Valve, even though their games have lootboxes, they got it [mostly] right by trying their best to make sure there's no "pay to win" (save for accidental cosmetics' bugs, which are half of the time are "pay to lose" and either way are typically fixed promptly) and all game mechanics are equally accessible to everyone from minute zero, with lootboxes being purely cosmetic.
it varies immensely, and honestly there's no consensus among gacha players what f2p even truly means. It could mean that you can experience all content and eventually pulled some desired characters without paying (e.g. no paywalled characters nor features save cosmetics). It could be more based on a vague metric on how competitive a free player can be in the game (e.g. obviously not going to be top 100 in most games, but maybe top 1000 for a player who plans). It could mean you get a lot of pulls and can grab most of the roster without spending (with whales going for dupes to make money). etc.
People will probably argue about it until the end of time, and I dont particular care to give my take on it. Just wanted to share a few other perspectives.
As much as you'd like to prove it's a different animal, the game's design was corrupted in that case as well.