No, but it means media companies have a responsibility to their users to handle these carefully.
Probably needs a bit more research what kind of portrayals of suicide have that effect. Then yes. Content is banned from most impactful media channels for less.
It serves as a very interesting test, either for those who want to limit some rights for safety reasons who fail to apply that logic here or for those who want to limit suicide as a topic for safety reasons but fail to apply it to other rights.
No one would care if this were just a story about suicide. This is a story that sympathetically portrays a girl who kills herself to make others feel sorry for her.