The tone is up to you. You decide the story, you decide the tone. It can be an incredibly sad story, if you want. It can be a silly story, if you want. It can be a serious story, if you want. It can be a happy story, if you want. We're not enforcing the tone, we just don't want our jam to exist as an incentive for people to create stories that make people feel more worse after they finished it than they did before. Does it have to be necessarily uplifting per say and happy? Not at all!
We wanted to make things vague enough for people to have a great source of freedom to express their stories in whatever way would best suit their narrative and message. They're stories about mental illness, so sensitive topics are likely going to explored and we don't want people with mental illness to find themselves ruminating on the negative aspects too strongly, ergo cyclically reinforcing the negative aspects of their mental illness. The story can be upsetting and doesn't even have to have characters overcome their mental struggles - but we don't want it to be in a pessimistic light that serves as to affect the reader in a bad way. I hope you understand what we mean.
Re: Intention and sincerity - we want this to be a story that you, the creator, puts your heart into. It's not exactly easy to quantify that in terms of tangible content, but there are certain aspects of a work that can shine through regardless of surrounding elements. We didn't want to be too constricting when it comes to a theme. Yes, the underlying baseline is queer characters with mental illness, but you can go so far with that and do whatever you want... as long as it's true to you. Make something worthwhile. Make something you believe in. Make something you love. We want the love to shine through to us, and the reader, as well.