Any success stories after a failed appeal?

OP, the bottom line is that it is necessary for you and your child to move on from this set-back.
That may sound harsh but by continuing to think about things in terms of getting what you and your child want, you are simply perpetuating the agony of the decision. As others have said things normally do right themselves and after a few weeks at school, there is no issues at all. I recognise that too many things are not normal at present but for the sake of your child you need to present as normal to her, so that she can start to move on.

They are both thriving

Actually, we had a similar situation this year with twins, one with SEN. We read between the lines of the information that came from the primary school, and separated them between two different schools in the MAT

Better for everyone that they are separated

From your opening post, it sounds like 100% the right decision by the appeals panel. Absolutely no way should any child start secondary school with another child ‘relying on them for pretty much everything’. Any hint we get from primary schools or parents of that sort of relationship, and the children will be split up as distantly as possible, and if that is not possible in one school, then it may be best for the ‘dependent’ one to go to a different school.

If you told the appeal panel that your child relied on her friendship group, then surely you can see they are not going to want to admit her. It would be horrendously unfair on the other children she ‘relies’ on.

Our appeal was also unsuccessful too. So sorry things didn't go how you wanted. It's such a stressful time.

We have put the failed appeal school to the back of our minds now and looking ahead to the allocated school now. DC isn't looking forward to it at all but are making the best of the situation and I'm sure all will be OK.

Our appeal was successful based upon social and medical due to SEN and anxiety. We had letters of support from my DCs Ed Psych and his psychotherapist which I think made all the difference to be honest. They both explicitly stated that my DC had a greater need than other children to be placed with an already established supportive peer group. If you can appeal again I’d try to get professionals on board, we went private as the waiting list for CAMHS is appalling here.
I feel for you, it’s incredibly stressful

It’s not about how much the panel cares. The panel has to operate within the parameters of the appeals code and has to weigh up the detriment to your child in not getting a place and the detriment to the pupils already in the school if they have to cater for an additional pupil.

I surmise that your appeal mentioned friendship issues, which wouldn’t usually be enough to win an appeal, unless you had a letter from CAMHS or other health care professionals confirming that in their professional opinion your child needs to remain with their friendship group to help manage their anxiety. It sounds harsh, but appeals on medical/social grounds usually succeed only where the parents can show that the school is the only one that can meet the child’s needs.

As others have said, you can appeal again next year, but your best option might be to pursue an EHCP that names the school.

You have the basic right of appeal once for each academic year, so if you don't get a place from the waiting list in the meantime, the next time that you can appeal is when the school / LA opens up applications for her year group to join year 8 - usually round about this time in year 7.

But as pp have said, the thing to do now is to get her (and yourself) as enthusiastic as possible about the school that she has been allocated - you can describe it as the school that chose her, perhaps? - and make sure that the school knows about your DD's concerns.

And presumably she can still see her primary school friends outside of school, even if they go to different secondary schools?

I have seen it hundreds of times, teaching and having my own children go through the system. We live in an area where parents become very fraught about secondary schools and there’s a lot of stress in year 6. There are tears and appeals and people move house and consider going private. But hardly anyone is still worried by Christmas of year 7. Most children are absolutely fine. Although it seems very worrying now, friendships almost always rearrange in year 7 anyway, even if they come with established groups, so it may be less of an issue than it seems at the moment. It’s important that you show your DD that you believe it’s going to be OK at school number 2, even if you do continue trying to get her a place in your preferred school.

The thing to do now is to be positive about the school she's got. Ask them if she can do a daytime tour or an additional taster day there to get a feel for the place (is her year doing a day there anyway, they may put on additional days for students who would benefit from this). A daytime tour, even one for just an hour helped my DD when she didn't get her first choice - the Head of Year took us round.

If you know that your child will be using the Student Support Services (or whatever term the school uses) can you get in contact with them or the SENCO and arrange a meeting with your child to look round there as well? Get an idea of what support will be available for her.

We didn't get our DD's first choice and our appeal didn't succeed. She's fine where she is and made really lovely friends straight away. Do not blame the panel for not putting the appeal through. You can stay on the waiting list of the preferred school but may never get to the top so I do think it's better for the child to know where they will go now and work towards that.

So sorry to read this OP. I do know that my DCs' secondary school is not the first choice of a lot of local parents as they apply (hopefully) to the outstanding secondary in a nearby village. They are out of catchment so don't usually get in, and end up at the local school as a second best. AFAIK in all cases where I know the family well enough, it has turned out fine.

Your case sounds different tho - in my examples most parents were "ah well, worth a shot" and accepted the local school with its advantages of being within walking distance and local friends.

Where is the school you have been allocated? Was it on your list? Is it your local school so she will be able to walk there? Can you try to talk it up in those terms?

Also I believe you are allowed to appeal again (I am not an expert) - by which time you may have some more convincing medical evidence to support your appeal (I think it is you that said you hadn't been able to get DD assessed bc of COVID?). Where are you on the waiting list, any hope there?

Really tho I would try to get her enthused about the offer school - uniform, subjects, clubs, find out if anyone she knows is going there.