Bless her, sounds like she's finding ife difficult. Quite a ot of the things you mention do hint at autism? Females mask very well and t can be difficult to spot, but struggling to socialise with peers, no real interests, general sort of fatigue about life, opting for a bland/not great diet, wanting friends but not really knowing how to form and maintain friendships, struggling with/not liking phone conversations, not particularly into fitness, perhaps feeling more at ease around an older generation bit then feeling on the periphery, gaming ...
Maybe have a look into it, the GP could help with an asd assessment although it does take time. Reading around a bit and researching yourself about females with ASD, there are lots of free online courses including level 2 understanding autism that might help you and her to understand her difficulties are quite common in autistic folk ... From there, you'd be able to look for local support groups that might attract similar mindee teens. Just a thought. I was very similar to this as a teen, never felt like I fitted in an always felt a bit sort of on the outside of life looking in, if that makes sense, unale to find my place.
Ignore me if you've already looked into this and discounted autism though, and my apologies for any offence caused.
Things that might help:
A therapy pet for sensory calming/relaxation such as an older cat
Spending time volunteering or helping in a nursery or l people home(ASD folk tend to relate well sometimes to the very young or very old and it may be an area of work she hasn't thought of)
Looking into relaxing/mindful hobbies she might enjoy that can be very soothing such as crochet, cross-stitch, or even mindful colouring/water-colour painting
A swimming pass or some kind of exercise equipment for at home if possible, as team spots and classes might be overwhelming / sensory overload but there may be some form of exercise she'd enjoy doing alone such as rowing machine, skipping ropes, weights with some links to online exercises that would help build her self esteem and release happy chemicals
Trying a little bit of cooking together at home and/or treating er to a little online nutrition course with videos and certification such as centre of excellence...
Best of luck, feel free to message me if you'd like to chat x