Depressed characters are still interesting characters, but you have to write them that way.
Speaking as somebody who suffers from dips into depression, you're absolutely right that writing a depressed character effectively, in a way that's interesting to read, is very challenging. It echoes the real-world struggles many depressed people face, in that you don't want to bombard people with a deluge of depressed thoughts and sadness and negativity - nobody wants to listen to constant pessimism, both in the real world and on the page. However, when you're an author trying to write that perspective, I feel it's important to point something out: depression is not always just feeling sad and sorry for yourself, and a depressed character is still a character worth caring about - but you have to remind the reader why they're rooting for them. Clinical depression, post-traumatic stress (PTSD), and the associated negative emotions come in a variety of flavors and can express themselves in many different ways, and to make writing about Alice's depression less of a slog for the reader and for you as the writer, it helps to embrace and understand the many ways in which it can manifest, and to emphasize that Alice is still a character the reader should root for, especially when she's going through such a dark phase of her life.
Here are a few ideas for how to make this character more engaging and relatable, while not taking away from the sensitivity of your portrayal of their depression.
Depressed people don't always act depressed.
It should always be okay to express your feelings to others, and it's valid if those feelings end up coming from a place of negativity and disappointment. But I learned early on, as have many other depressed people, that inflicting your depression on other people more than occasionally, and making it the only thing you ever talk about, is a surefire way to lose friends and feel even worse about yourself. Sometimes you need to just keep your wallowing and inner demons to yourself and put on a happy face, however painful it might be to do so. It's not fun, but it's just how it goes.
That's why it's important to remember that depressed people are often very good at masking the way they feel. They don't mope around or "act depressed" all the time. Sometimes it surprises people to learn that a happy, upbeat person is struggling with inner demons, because they "seemed so happy," but it never surprises me. It's easy to wear a happy face to work, to school, with your family and friends and loved ones. Taking it off is the hard part. You have to trust someone so much that you're willing to be broken in front of them, and that's something not everyone is ready for. As a result, the happiest person you know, the one who tries to see the silver lining in everything and is relentlessly positive, could be the one with the most struggles on the inside, and maybe Alice is like that too. Maybe she's able to put on a mask around her friends, and doesn't confide how she really feels until she's in the most vulnerable moment to do so - and if so, the moment she does finally let her guard down will be all the more significant and special.
Depression can be overcome, and coped with. It's not the end.
There's an old parable about a man whose oxen and cart get stuck in some mud, and he appeals to the gods to save him. The god dutifully appears and reminds him that he needs to first try his best to push the wheels and help his oxen himself, and then he can appeal to the gods for aid.
Your depressed character will be more engaging to the reader if they try their hardest to overcome their depression and move forward, however fruitless or difficult or painful that might be. Treat this obstacle like any other obstacle they would face, and use it for character development. Everyone copes with feelings of sadness, loneliness and emptiness differently, and Alice will probably have her own ways of dealing with negative emotions. Some people have unhealthy coping mechanisms like drinking or overdosing on medications, others play video games or bury themselves into hobbies, and still others go to therapy or have a dedicated lifeline that they use when they're in their darkest moments. What does Alice do to cope? How does she fight her feelings and try to overcome them? The answers to those questions will develop her character. Even the saddest person still has some agency as a character, and the ways in which Alice fights to overcome her negativity and sadness will be how she stays relatable and makes the reader root for her. She needs to show the reader that she's not giving up, and that the reader shouldn't give up on her.
Depressed characters allow you to explore interesting themes.
I think the best media representation I've ever seen about depression comes from the metaphor at the start of this Hyperbole and a Half comic.
I remember being endlessly entertained by the adventures of my toys. Some days they died repeated, violent deaths, other days they traveled to space or discussed my swim lessons and how I absolutely should be allowed in the deep end of the pool, especially since I was such a talented doggy-paddler. I didn't understand why it was fun for me, it just was.
But as I grew older, it became harder and harder to access that expansive imaginary space that made my toys fun. I remember looking at them and feeling sort of frustrated and confused that things weren't the same. I played out all the same story lines that had been fun before, but the meaning had disappeared... I could no longer connect to my toys in a way that allowed me to participate in the experience.
Depression feels almost exactly like that, except about everything.
Real-world depression isn't so much about feeling sad as it is not feeling anything. It's the emptiness, the void. When you try to do things that once brought you joy, the enjoyment just won't come. It feels like a gnawing pit inside of you, a place that's not even dark so much as it is nothing.
That sounds like a theme that might be interesting to explore, doesn't it? Everyone has that existential dread somewhere deep inside of them, and portraying a character suffering from feelings of emptiness will give you a prime opportunity to explore that side of your characters. Depressed characters give you ways to explore mortality, death, existentialism, loneliness, and so many other powerful themes through the lens of their struggles and thoughts. You don't always have to make the reader sad if you can make them think instead.
I hope these ideas help you with writing a depressed character, and if there are any more questions you have or things you want me to address from a personal perspective, definitely let me know - happy to help.