Depression can be caused by low levels of Vitamin B, especially B6 and 12.
I'd start by asking her some practical questions: would she like to feel happier? Would she like to feel more confident and capable? Discuss with her what her ideal of these might look like. Get her to describe it in vivid detail. Have lots of chats about how life would be for her in an ideal world. Then work backwards from there to work out what steps she could take towards feeling that way. Talk about the inevitability of failure and disappointment from time to time and the importance of having good self-care and self-compassion strategies to boost you when these happen.
There are some workbooks for helping teens with depression, anxiety, autism etc on Amazon. I'd just type in workbook teenager + whatever concerns you and her most in the Amazon books search list and see what appeals to you.
I used to ask my autistic son (who also had ARFID restricted food problems and acute social anxiety) to imagine walking into a party where everyone smiled and looked happy to see him and said hi to him. I got him to imagine this a lot, so he really could feel the experience, if only in his imagination. Then we worked backwards from that, discussing what might make that possible for him, and then I supported him as he slowly made adjustments to his attitude and behaviour that he chose to make, until now, exactly that happens!
Same with food. We discussed how he wanted to feel and we researched the impact of food on energy, mood etc. We made lists of all the foods that might help and discussed which ones he felt able to eat.
For example, if your daughter is able to eat breakfast cereals. I know they are unfashionable UPF but they have added vitamins. Rice Krispies or Special K in particular can be great sources of Vit B. If she likes chewy gummy sweets you could add a small packet of children's gummy bear vitamins to her daily food intake too. If she likes honey or marmite, they could help. If she likes banana bread, make some with half almond flour and a spoonful of dark molasses or treacle and a small finely grated carrot as well as the usual sugar to the mix. Each time you make it slightly increase the amount of treacle or molasses. These are good sources of Vit B, A and potassium.
I'd also offer bribes. I believe in bribes. We all do things for reward in life. I'd promise her a small treat if she can increase her independence. Make tiny changes. Where you usually drop her, drop her 10 metres further from school. Then 20m, then 30 etc until she is walking the last block to school herself. Or get her to leave the house on her own and walk and you follow in the car and pick her up when she gets to the end of the road, and then round the corner etc. Tiny shifts can suddenly speed up the process. It's time consuming for us as parents but it really pays off.