Yes, in Memento the main character leaves notes for himself, because he wakes up each day with no new memories since his "accident", but he is trying to solve a crime!
Whether the notes and the character's understanding of his situation are accurate is the main gist of the movie (and as its tagline says: "some memories are best forgotten"). I can't recommend it enough: it's a great movie with some excellent acting, and it manages to be both cerebral and emotional.
In Memento, Leonard doesn't lose his memory when he goes to sleep, he just can't form long term memories. This affects his whole day, Leonard can start a task or conversation and not remember starting it by the time he gets to the end.
There's a scene that starts with Leonard in a hotel room, sitting on a closed toilet, fully clothed, with a bottle of alcohol in his hands. He wonders why is he sitting there and if he's drunk. He then takes a shower. Because he doesn't know why he's in the hotel, he doesn't know why he's in the bathroom, etc. He literally forgot he broke into the room to ambush a guy as he was doing it.
Whereas in 50 First Dates, it is how you described. Lucy replays the same day, she resets when she sleeps. But during the day, she can recall what happens. She can tell you what she had for breakfast, where she got her pineapple, who she met, etc.
It's one of my favorite movies. Even knowing it beat by beat, I enjoy watching it because it is so well told. Even the narrative structure feels integral to how Nolan wants the story told. So it doesn't feel as "gimmicky" as it could be.
It also gives a nice twist on a noir murder mystery. Because the story starts with a murder, then instead of making us guess who did it, it makes us figure out why he did it. With every step giving another piece to that puzzle. So the mystery unfolds linearly while the narrative goes both backwards and forwards to meet back at the beginning of the movie.
While I haven't watched Dunkirk or Tenet yet, Memento remains my favorite Christopher Nolan film.
Whether the notes and the character's understanding of his situation are accurate is the main gist of the movie (and as its tagline says: "some memories are best forgotten"). I can't recommend it enough: it's a great movie with some excellent acting, and it manages to be both cerebral and emotional.