“Granting the appeal, Judge David Bean said he was persuaded "not without hesitation" that Harry's challenge has a real prospect of success.”
Also, as there’s been some confusion about this, the judge is not saying here that he thinks Harry has a strong case. He’s saying that, with some hesitation, that some of Harry’s case meets the threshold necessary to be granted permission to appeal (the test you need to meet being that you have a real prospect of success). A “real prospect of success here” means “one that is realistic rather than fanciful, and does not mean a greater than 50/50 chance of success”.
Harry argued that he had five grounds on which he could appeal. The judge rejected three and a half of these, and allowed an appeal on one and a half of them - as he said, not without hesitation.
But, Harry has permission to appeal. So he may be successful. It is more likely he won’t, but litigation can be a lottery!