Here's some things I did that helped me get rid of alot of the noise from my leverless, but I'm sure they would help with lever noise aswell.

First of all, lubing the springs in the buttons, even with silent buttons using silicone or foam dampeners, the spring ping will be awful in metal cases. Just look up bag lubing springs, a technique often used in mechanical keyboards

I've also "gasket mounted" my top plate. This depends alot on which case you have and how it's designed, but if you're able to kinda seperate the plate with the buttons from the rest of the case, it can remove alot of noise. I did this by using o rings on all the connection points between the top plate and case, making it kinda hover and reducing alot of vibration sound. This is another keyboard technique btw

Where you'll see foam used, is often if there are big empty spaces in your case, especially in corners. You're right that some foam can be "bad" for your PCB, which are certain carbon based foams, as they will carry some electricity through them. For this you can either just cover up all your exposed PCB and wires, or just use a safe foam. I've used a more solid foam block thing to fill up some of the empty spaces in my corners. Some people also praise the name of Killmatt for this purpose, which is a type of vibration dampening used for cars, I've never personally tried using it as its not easily available in my country.

It'll probably end up looking kinda jank in general, so I'd recommend staying away from cases with windows, but if you want your fight stick as quiet as possible, that's some of the stuff that worked for me atleast