Following Mindful suggestion here, I'm opening this question following that one: in there, Mindful explained that the main difference between 「つぶやく」 and 「ささやく」 is that, I quote:
you want 囁く when you are talking about whispering something to someone. 呟く on the other hand is also often translated as mumble or mutter, English words which better express the idea that the thing being said is not intended to be heard by anyone but the speaker
My doubt arises from short stories I'm reading, in which 「つぶやく」 is used when a character is speaking with another, seemingly with the intention of being heard, and the other characters seems to hear it:
In this case the girl is asking the protagonist to walk her home, and it doesn't seem she doesn't want to be heard; the character does hear her.
So I was wondering: does this have any implications about the speaker not wanting to be heard, or 「つぶやく」 can just be used to speak to others?
Edit: a little more context: as far as I can understand the only relationship between them is professional, both work at the same restaurant; a little later on she says that she always asks for early shifts because she is afraid of the night (夜がー怖いから), but that day she had to stay until late, so the request to be walked home seems to be honest, not just a front to keep the relationship. Here's the page: https://i.stack.imgur.com/FNXjg.jpg.