I have a bit of problem with writing my mute character, she supposed to be somewhat of a mentor role and she was born mute and she use her phone to "talk" a text to speech app, but I don't how to describe her talking, I guess the most I came up with is her having trouble communicating due to people mistaking her for playing on her phone when she's trying to speak
Have her use sign language, and have her use facetime on her phone.
Consider making use of facial expressions and body language alongside sign language and written text / text to speech to augment her communication skills with the speech-capable people that don't know sign. Perhaps laminated notecards with pre-made, common phrases on a keyring she can just pull out when dealing with others face to face. something to quickly get across the point of "hey I'm mute. be patient while I produce a reply you will be able understand".
You can also differentiate her words from others by italicizing it! So, for example:
"Hey Character A, how's it going"
Character A shrugged, typing out a response. "Could be better."
I have a character that's almost exclusively selectively mute (she speaks very rarely except to her father figure), and since she's young and doesn't sign or have a phone, other characters have to play a guessing game as to what she actually wants. She's very vocal in the way she isn't because I really emphasize her body language. I pulled a few examples from a short story I wrote with her:
-She paused at that, clearly contemplating the offer, before instantly brightening and bounding over to grab his hand.
-Pip pouted and tugged on his sleeve pleadingly, but he shook his head.
-She sighed dramatically, then shook her head.
-Pip held up two fingers, indicating the second option and bouncing with excitement.
My personal advice is to focus on conveying meaning and emotion more than actual words. Good luck finding something that works for you!
One approach you could take when describing your character's communication is to focus on the nuances of her text-to-speech app. For example, does the app have a robotic or monotone voice, or does it sound more human-like? How quickly or slowly does the app "speak"? These details can help create a more vivid and unique portrayal of your character's communication.
Additionally, you might consider exploring your character's body language and nonverbal communication. For instance, how does she express emotion or convey complex ideas without words? Does she use gestures or facial expressions to supplement her text-to-speech app, or does she rely solely on the app for communication?
Finally, don't be afraid to address the challenges your character might face in a world where verbal communication is often taken for granted. As you mentioned, people might mistake her for simply playing on her phone, or they might not take the time to listen to what she has to say. Consider how these obstacles might affect her relationships with others and how she navigates the world around her.