Not sure what I am looking at. I believe it is the backsplash to countertop but???? Bad caulking job is all I see. Is that a raw tile edge on the countertop backsplash? Anyways take a few pics further back for context please.

It's not the best caulking job I've ever seen. It should be much smoother and smaller. Would suggest you have it redone.

What type of T&G did he use? T&G normally would not have a gap like that? All I see is that catching crap and being nasty (wood in general is a poor backsplash for that reason). And you already had a 4" backsplash.

This might be too bulky for your application, but we used the smallest shoe molding to finish off the inside corners of a part paneled and drywalled bedroom. These are close-up photos, the texture that is pictured in the second photo is just normal up-close texture that would occur from a paint roller. From a distance this shoe molding is hardly noticed once painted. I would install the molding and then apply the thinnest paintable caulk as needed around the sides of the shoe molding to fill any small gaps before painting. I would run the pewter green molding into the shoe molding rather than notch the shoe molding to accommodate the pewter green molding.

If it is determined that shoe molding would be too bulky, I would redo the caulk--hopefully the gap between the two walls is not too wide.