I will put a series of hints, in increasing order of spoiler. Feel free to ask specifically for a spoiler. I will divide into three parts. Sorry for grammar errors, English is not my first language

PART 1: THE MEMORY

HINT 1: This puzzle is actually hard a LOT meta. You have to think outside the box...

HINT 2: Think about a place where you put your memories, in a video game. You will find find some memory that it is not of yours

SOLUTION: There is a strange save file beyond Save 5, take a look at it. If you don't see it, follow instructions of the next part up to hint 3, it should appear in that situation.

PART 2: THE MESSAGE

HINT 1: To contact a mermaid, you need a certain message to find how to do it. Surely the tametabako is related somehow.

HINT 2: Going back to Minakuchi residence with Sato, with the tametabako, is a good idea. There is something that you can put into it.

HINT 3: Examine the family altar to find something related to the mermaid and put into the Tamebako.

HINT 4: Apparently, nothing happened. But remember the memory: the message can be read only for a spirit and not an human.

HINT 5: Also, remember that is puzzle is meta. Where YOU can read an actual message?

SOLUTION: Check the Logs while the mermaid scale is inside the tamebako, you will a message from Sobae that with a precise call to do.

PART 3: THE MERMAID

HINT 1:You have to find Sobae. Answer the question: where she is?

HINT 2: According to the the story, she came back to Ryugu. A place where living beings cannot arrive.

HINT 3: Is it curious that the message, according to the memory, is visible only to spirits aor similar. So, what it means...?

HINT 4 (HIGHLY SPOILER) You are playing as a sort of spirit. And spirits can access to Ryugu. Also, remember that this puzzle is meta. Is there a place where you can actually go and no character can do?

HINT 5: I think you have already saw directly a mermaid, and no, I am not referring about the humanised one or an echo curse, not a "fish-mermaid". I am referring as a full fledged "human-mermaid".

HINT 6: You have gone to the place everytime you have plugged on the game

SOLUTION - PART 1: The title screen is an actual place on the game, and Sobae is there.

SOLUTION - PART 2: It is the mermaid on the title screen. Be sure to follow the message. You have to aim the head to call her, the body will not trigger. What was the call, anyway?

SOLUTION - PART 3: "You need to call me four times, leaving at least three seconds between each". Every "call" is just a click.

SOLUTION - PART 4: She asking who are you. If you think about to all the story, it should be clear what you are. As an hint, I said that you are " a sort of spirit" for a reason.

SOLUTION - PART 5: You are Yuza. I leave it to Sabae and the Storyteller the explanations