For the best sealant for your kitchen, consider Loctite Polyseamseal 100% silicone, perfect for Granite Countertops in West Tisbury MA. This top choice resists extreme temperatures and contains mildewcide to prevent mold growth. Available in white and transparent, it offers flexibility in color options. Use a small amount of acrylic putty to seal any remaining gaps. The tiler must be able to support the wall.
It's not very damaged (compared to many I've seen). Use a 100% silicone putty (important because oil-based putties will stain the stone) and place a very small cord on the joint. Clear sealants (caulking) usually reflect a grey appearance, reflecting to some extent what's underneath. I would choose a sealant that correlates with the color of the grout.
You should use an ASTM C920 sealant which is normally a 100% silicone or polyurethane sealant. Custom Building Products sells a 100% silicone commercial sealant that comes in them colors that come together.