Are you looking for a room divider? [houzz=] [houzz=] [houzz=]

Already you have left space for 18mm thk single glass.. to insert inside the hollow gap.. A;so a electrical wires in been kept on top, i dont know how u where u wanna used that for, there is no sandwich type glass space over there... Wood u hav already used for panelling & u r looking for glass.. wat type to take... My suggestion will be, u go for clear toughened glass, so that on one side u can fix film, ,,, so that any time if u feel like to change the design u can. but if u for for designer glass or decorative glass, which will not alter later, that will be one time large investment for u ,,, But changing the film will not disturb the entire partition and glass , only reasonable price u can change the entire film as per latest trendz

Temporarily you can lay a thin bead of caulking it will come off both the fridge and counter cleanly. Not seeing the issue and possible space it's difficult to advise you further. Possible to take a picture?

you could also do french doors. either with windows or without. Don't know if you could do a pocket door. that's the sleekest option but more work.