Im 50/50 about her "lotsa people in my hear" being metaphorical for self doubt, or if this just became a multiple personality disorder awareness manga.
It's the former, almost certainly. Nothing else about this title speaks to mental health, including the resolution we've been given. Even axed, I'd expect some more-explicit indicator of mental stuff was the aim by the mangaka.
People of all stripes have all manner of sides to them, and more so during puberty when trying to "find themselves / determine their identity".
This was a title that explored that literally by taking those facets of Karin and manifesting them as individual people via Shrine Magic.
And Karin hating herself, was due to her being alone without her best friend in a strange new place, dealing with anxiety and uncertainty, and all the expectations and pressures of adolescence in school pushed her to spiraling until her Wish manifested and she fractured before seeking out Yuu to fulfill his side of the wish, and the events of the manga play out.
**I'll edit to add on that - it
is dealing with mental health, but the kind that probably almost everyone who goes through puberty goes through - the social & developmental stressors and events that coincide with that part of life. But I'm very, very confident that it's not dealing with the type of mental health that involves psychiatric assessments and intensive medical intervention.