Player vs PC
In most games, the relationship between the player and player character is presumed to be 1:1. The PC represents the player in the game world, and/or the player's choices are determining the PC's actions. These games complicate the player-PC relationship by adding a level of removal or metafiction. Spoiler warning as in many of these games this is a plot twist.
Type A: The characters are aware of the player as a sort of extra-game-world entity.
Type B: The player is not literally an entity in the game world, but the relationship between the player and PC deliberately mirrors a metaphysical process happening in the game (e.g. possession or time travel).
Type C: The player assumes they are playing as the main character, but actually they are playing as a different character (may overlap with Type B).
Type A: The characters are aware of the player as a sort of extra-game-world entity.
Type B: The player is not literally an entity in the game world, but the relationship between the player and PC deliberately mirrors a metaphysical process happening in the game (e.g. possession or time travel).
Type C: The player assumes they are playing as the main character, but actually they are playing as a different character (may overlap with Type B).
17 Games
Type B (arguably type C): The player's name is the name of the fallen human, and your actions determine the purpose of the fallen human's presence in the world. Flowey talks to the player as if they are the fallen human.
Type A: Monika is pursuing the player, not the PC.
Type B (arguably type C): The player's progression through different routes mirrors Akane's exploration of different timelines.
Type A: The game world is explicitly a simulation being run on the player's computer. Many of the characters see the player as a sort of god. Others speak directly to you.
The lightest Uchikoshi example: very, very minor type B references (remembering things from previous routes). Almost all of these are plausibly deniable due to Date's amnesia.
Type B, via the branching routes, allusion to type A at the very end.
So far it seems to have some of the B/C elements of Undertale, though the "character creation" might also end up being type A.
Type B: Branching nodes/time travel.
Type A, with the concept of the Frayer. Some continued type B references from the previous game on Mizuki's route.
Type B/C: The player controlling York mirrors Zach's relationship to York; York talking to Zach often seems like he's addressing the player, and only later is this complicated.
Type A: Player is a rogue element in the characters' universe, and some characters seem to be aware of them.
Type B: exploring game routes mirrors the protagonist gaining information and attempting different sequences of events during a time loop.
A/B/C: You're playing as Lila possessing Will. Implication that the whole story exists so the player will think about Lila, perpetuating her existence. Interestingly, there are other NPC characters who are meant to represent the player.
Type A (/type B, if you interpret it that way) via type C: Routes are time travel, "Blick Winkel", and two levels of not playing the character you think you're playing (by way of player possession and characters deliberately misleading the player).
Type B: The player controls the party's "guardian spirit", which is a superficial distinction until it isn't.
Type A: Much like AINI, the Professor specifically talks to the player as an-extra game entity. Terry also tries to fight you.
Type A: PC explicitly breaks the fourth wall, asking you to solve the mystery as her "string-puller" by save-scumming through different routes and reporting back to her.