The solution is Photoshop needs to be launched through the Ayon launcher
For what it’s worth - it’s good to note that all applications only have the integrations active when launched via the launcher. This is not Photoshop-specific but also goes for Maya, Houdini, Fusion, Nuke, After Effects, Resolve, Blender, etc.
Ayon does not install itself into your local installs of the applications (you can run them fine outside of Ayon without the Ayon tools). But instead only loads up the relevant bits when launched via the launcher.
There are some edge cases, e.g. where for Adobe products the plug-ins MUST be installed locally for Adobe to even consider them to work, so there may be potential ‘traces’ of Ayon. But the mean goal of Ayon is that it should not affect your applications itself when not launched via Ayon - if the host app allows that.