I'm sorry to hear that you are having trouble with JuiceboxBuilder-Pro under macOS 14.6.
Which is where it's been for every previous version. Juicebox refuses now to remember this.
What is the directory that it defaults to now?
What if you change the presets folder to something different and then try to load or save a preset? Does it remember the new path? If not, what directory does it show?
The presets folder being 'forgotten' certainly sounds like it could be some kind of permissions issue (perhaps a failure to save the path due to a change in macOS 14.6) but I fail to understand why the Publish button does nothing. The Publish button (Start -> Images -> Customize -> Publish) should just change the current panel to the Publish panel and this panel change should be no different to clicking Start, Images or Customize (other than the resulting panel being displayed), all of which sound like they are working fine for you.
I really don't know if it will help but please try the full uninstall/reinstall procedure outlined as #11 here, especially deleting the ELS folder between uninstalling and reinstalling (which should reset the presets folder to the original default path).
Also, please double-check that you are using AIR v33.1.1.744 (the version with WebKit support).
I hope these suggestions help.
As always, please let me know how you get on. Thanks.