S.T.
i'm sorry your daughter is experiencing this. i can only imagine how difficult it is for you to watch her struggle.
you've done the main things i'd have suggested, to enroll her in extracurricular activities, and get her counseling. i'm not sure they've actually failed. sometimes you need to push past what (or who) doesn't work.
but the main thing i'm seeing here is that your love and fear for her is causing you to take on her struggle. and it IS a struggle, no mistake.
the problem is, it's not yours.
you can be supportive and empathetic, but ultimately it's your daughter's to fix, tweak or learn to live with. and your support and empathy need to not tip over into managing.
yes, girls can be cruel and catty, but they're not all that way, and i'm glad you recognize it's likely to be an overabundance of neediness and/or desperation that is turning off potential friends.
the most essential (and hardest) thing for your daughter to internalize is how to love and be proud of herself, and if necessary, sufficient unto herself, at least from time to time. and that, unfortunately, doesn't happen from her loving, anxious mother just telling her how wonderful she is (not that you appear to fall into this trap.)
she's sitting alone at lunch? take a book. not a phone or a device, an actual paper book. not only will it take away the loneliness of sitting there by herself, it will make her lunch break actually pleasurable. it may also have the side benefit of attracting other bookworm friends, but if it's nothing more than a ploy it will backfire.
reading while dining solo is an introvert's bliss. your daughter may not be an introvert, but she can still cultivate this extremely useful coping mechanism.
keep enrolling her in extracurricular activities, but not to make friends. she needs to explore her interests AND expand upon them. the activities themselves should be the draw. friends may or may not be an unexpected blessing, but if she's absorbed in caring for unwanted animals at the shelter or helping at a soup kitchen or beautifying a veteran's cemetery or learning to run a potter's wheel or hand-dyeing silks or riding ponies, she'll interact with others at the very least and learn to value her energy, commitment and sharing qualities as well as expand her interests and abilities.
all therapists are not created equally. 'pro-activity' is not always a desirable quality. you don't necessarily want a therapist who is going to proactively fix your daughter. a passive one who quietly edges her out of her fears might be better. regardless, if the one she's seen isn't suitable, find another one.
consider finding her a big sister or big brother. you are wise to recognize that you are being drained, and that she needs mentoring outside your tight little loving family unit. another empowering adult in her life might be just the ticket.
while i'm a loud proud homeschooling advocate, i think this is exactly the scenario where homeschooling is NOT a solution. not only could it be isolating (my kids were actually far more social in their homeschooling circles, but you have to work at that) but it will throw her even more solidly onto you as her sole resource.
i really love that you're not a coddler, and that you're looking for ways to strengthen her. she does need you as her soft place and sounding board, but you are completely correct in refusing to let her fall down and give up on top of you.
you can do this, mama. i've got faith in you and her!
khairete
S.