the key evidence is the medical evidence. Without evidence of murder the circumstantial data is irrelevant
No, you have misunderstood about how juries use evidence to reach a verdict. Circumstantial evidence is the basis of most trials. Unless it's an eyewitness account or a confession, it is circumstantial evidence. Eg DNA evidence is circumstantial evidence. So, as we did not have a confession, a lot of the medical evidence presented to the jury here was circumstantial evidence and they were asked to judge whether the big picture of evidence made them sure that Letby did it. The medical evidence was part of it. The digital and swipe evidence placing Letby at each incident and showing she had opportunity and means was part of it. Letbys own evidence was part of it. The evidence about her character was part of it. The jury were sure.
The appeals judge was asked, was the expert evidence sound? Was Letby's defence adequate? Is there any avenue for appeal? They said yes, yes, no. I will be v surprised if anything comes of this, as there is only one option left. Of course Letby was always going to take it - what has she got to lose - but a bit of drumming over social media won't suddenly magic up a new avenue of appeal.
I think she will have run out of legal aid now so will be relying on pro bono work for this last try. She hasn't ditched Myers - he's doing the last bit of work she can get aid for, the Baby K appeal. So whatever the posters here think of his defence, she's happy with it and presumably would retain him for the next leg if she could afford to.