Is there a silent way to switch a 120v device on and off, the click of the GE wall plug is too loud for my application, something like a solid state relay?
Every relay is going to click. I have Qubinos, dry contacts, and numerous brands of switches and they all click. Even smart plugs have a click. Not sure you will find anything because even dumb switches click to some degree when you flip/toggle them.
What’s your application?
If this is something like not waking up an infant or a person with PTSD, the only two options I can think of is to instead install a dimmer switch (they don’t typically use a physical relay and should be quieter) or to use an inwall micro placed in a junction box elsewhere in the building.