What to do with ground wire in a double gang dimmer switch
You don't need to do anything. The switch will pick up ground via the screw heads of the mounting screws.  (this &quot;via the screw heads&quot; trick does NOT work for receptacles).
If you really want to attach the ground wire, then find the screw hole in the back of the box that is tapped 10-32.  That is specifically for a ground screw.  You can't use screws tasked with some other purpose.  You can drill and tap your own #10-32 hole, or you can use a grounding clip on the edge of the box.   Of course you don't have to do any of these things for a switch or self-grounding receptacle.
Now, that thing you're doing with the wood blocks is not allowed.  You cannot make a &quot;box extension&quot; out of wood, because the job of a junction box is to contain fires from electrical arcing.  Wood would only accelerate such a fire.
I gather you have been using wood screws to mount the switches on the wood; instead use 6-32 screws to mount it to the metal.  Further, you will need a metal box cover so the box is fully encapsulated in metal.
If you really, really need the switches to sit prouder than that, you can either rework the box with a taller &quot;mud ring&quot;, add a Legrand Wiremold Surface Conduit Starter Box as a 1&quot; box extension, or add something like a Hubbell PTC200GY switch extender, which is made to be a weatherproof outdoor cover for switches (but if you only use it as a spacer, I won't tell :)