I realised why Ami might be aware of the reset stuff: during beachmas she tells that she has a secret journal somewhere in the house, and the physical things like items made by Io do persist through resets. So even if she loses her memory, like everyone else, she will be able to remember a lot of forbidden knowledge by writing it down in a diary
Hmm I was on the premise that any physical clue deliberately left to remind themselves about the existence of resets will be gone with the reset or got scribbled by angels, especially if a Sensei met his early game over and everything got hard reset to square zero. Even if these clues somehow lived through a reset when the owner didn’t, I imagine they would just be weirded out and still couldn’t piece the lost puzzle together themselves, kinda like Futaba’s reaction to her unexpected poem (I just personally feel like it’s too anticlimactic to be a solution for reset lol)
However, this can still
kinda work if Sekai's journal somehow already had some super duper secrets about this strange world we now dwell in forever; and Ami would get "updated" if she found it within the cycle.
In fact this prompted something else in my mind: Maya's
gamer guide for day1 Sensei (the one item that may actually fit your description).
If we assume that a hard reset sends you back to absolute square zero, why wasn't that creepy diary gone every time an iteration die? It's not something the OG Sensei already had and we already know this diary didn't even exist during the first few cycles.
So it's either a special item that lived through all hard and soft resets despite not being in his room from the very beginning because...
Maya, or Maya just finished hauling ass handcrafting a creepy journal and putting it on your table when we "first" met her in
A New You.
Edit: nvm; Ami tells you to check on that journal before you even walk into the bedroom; so this probably is just a convenient "patch" that the world decided to keep for later Sensei iterations' sake (come to think of it, Ami is
okay with Sensei keep this kind of diary??? Maybe she just thought it was a benign list of names and details without photos).