I experienced this "setup failed" pop-up too. I have all three Affinity apps and have successfully updated Designer and Photo. After reading through this thread and tried the suggestions, I realized that I have lost all rights to the Publisher folder (and it had zero bytes). Tried to delete it but no use. But I just did a restart and the Publisher folder was not there anymore. I did an install once again (run as admin) and it worked. All is fine now.
P.S. ...This may be relevant or not, but just more info: Before I restarted, I deleted the Publisher Beta folder (so if you were a beta user, maybe you could delete that).
Sample images attached! I used the same image (from Pixabay) with the default settings in each case, except for a couple of the distortion effects where one of the slider values was an enormously long number instead of being not greater than 1.
julz got a reaction from Leigh in Publisher Update - Setup failed