You cannot paint tile. Just staining the grout is not going to make that tile work with that floor. You need to remove all of the tile and extend the wood. They clash pretty badly currently.

I would tear up the tile and extend the wood

The floor is nice but I'm wondering why you chose grey when you knew that you wouldn't change the tiles. Painting the tiles will not look good and in time the paint will peel off. Painting the grout will last but you will still have the beige tiles. Buy more flooring and continue it in the kitchen , what is the colour of the cabinets?