It is well known that the Sun has been settling claims - not just from Prince William, but large numbers of other claimants - for the last decade at least.
Harry’s issue wasn’t that people don’t believe the Sun hacked phones, it’s that he waited too long to do anything about it. So he can’t now bring a claim, and has no leverage to get a settlement. The implausible, unevidenced “secret agreement” was something he dreamed up to get around this problem. It was always a very unconvincing story, and one that the Judge agreed was not remotely plausible.
Harry wanted to have his day in court on phone hacking against the Sun. If you are seriously suggesting that his legal team decided they needed to rely on a secret agreement to be in time, but despite this would not bother to take any reasonable steps to prove it actually existed, despite having many options at their disposal to do so, I think you have completely misunderstood what’s gone on here.