Before the employee took action in tribunal they would have had to go through the trust's grievance procedure. The fact this went to tribunal suggests that the trust believe there was no breach of the Equality Act.
Once the employee started a tribunal case, the trust presumably took legal advice which told them there was a significant chance they would lose (which is not the same as saying they definitely did breach the Equality Act). The legal advice would have told them how much the employee was likely to be awarded. Taking this and the legal costs into account, the trust has clearly decided to offer a settlement to the employee. The settlement offered would be less than the amount the employee could have been awarded by tribunal, saving the trust money as compared with going to tribunal and losing but costing them money if they would have won had the case gone to tribunal. The employer would almost certainly have stated that the offer was being made without an admission of liability.
The employee then had the choice of rejecting the offer and going to tribunal with the possibility they might get a higher award. Alternatively they could accept the offer, avoiding the stress of a tribunal hearing and the possibility that they might lose and end up with nothing.
In this situation, since the trust is not admitting any wrongdoing, it is fairly normal for both sides to agree not to say anything about each other.
Once the employee started tribunal action, the only choices for the trust were to either arrive at a settlement with the employee or defend the action. That's what I was talking about when I asked what you think should have happened. Since you appear to be against them settling, perhaps you think they should have defended the action and tried to ensure the employee received no compensation at all.
I don't see settling as misuse of public funds. And settling with the employee does not preclude the trust taking action against any staff that caused the trust to breach the Equality Act, although I suspect the trust continues to believe that it did nothing wrong.
Once an employee has taken their employer to tribunal the future relationship is always going to be difficult. You clearly feel that the employee was mistreated. You may be right. But I am not surprised the employee was offered a settlement agreement to leave.
The NDA will not (indeed, cannot) prevent the employee from whistleblowing as I've already commented.
By all means refer this to the spending watchdog and/or the EFA. But personally I doubt you will get anywhere with this.