I sympathise with you, It's incredibly hard to be a good parent when you are fighting severe depression.
I would maybe chat to her about bucket lists. I used to ask DC what they would do if they had £50 to spend on an outing, or what outfit they would buy or what would be their dream dinner/cake/playlist.
Then I would try to set up some of these things for them. Surprise them with their dream dinner or when they were bored, help them put a playlist together, or take them shopping and give them money for a new outfit. Some of these things cost money, many cost time and attention. Talking about 'my ideal/dream' anything is quite addictive for children at that age as they move towards adolescence and think about how they'd like their life to be.
Spend time on her. Pay attention to what she loves and is interested in. One thing you could do is work on a Pinterest page with her to create ideas for a new more 'grown up' bedroom for her and then decorate it together - paint the walls, build the furniture etc. Explain budgets beforehand.
And you could create some rituals. We did family film night. Made our own popcorn and our own pizzas, then closed the curtains as if it was a cinema. We also did games nights. And DS and I went swimming together once a week, setting ourselves goals from 10 lengths when we started to swimming a mile by the end of the year. Every week we added two lengths to our total, then messed about in the pool for a bit doing handstands and went for a Sprite at McDonalds afterwards. Kids love rituals like that.
You could invite a handful of her new friends over for a pizza-making party with a film and a sleep over, then a pancake breakfast. Showing interest in who she is now, and who she is turning into is a really key bonding thing with tweens.