What objects are available for triggers

Workbench, as you appear to have been using, was the correct tool. The fact that permission set didn't show as triggerable told you what you needed to know. Unfortunately, that's the behavior of how Workbench works. Below, you'll see a screen capture from Workbench looking at User which is triggerable. Workbench only shows the information if an object supports triggers and omits it if it doesn't.