Frankly it would seem they don't even need to go there.
The basic grounds for appeal:
Bits of this judgment are fictional.
It looks as if a judge and panel in a very high public interest case with a judgment that was going to be gone through with a toothcomb, didn't realise this.
It's actually a possibility that they used AI to write it.
It's incompatible with the SC Judgment and is attempting to re write something it has no authority to do.
It suggests that things are legal which in fact are not.
Two minutes to: this judgment would appear to be compromised beyond standing.
The interesting bit will be what they do about it. I would hope SP does not have to go through the entire process again for her sake.