I think I read this wrong the first time? You are not asking whether or not to tile the 90 degree corner wall, you are asking actually how to finish the tile in the corner? We had one corner where backsplash met wooden pantry wall, we just ended it with tile, and then caulked, not grouted the end.

Inside or outside corner?

It's an inside corner. We are not continuing the tile past the corner, but I don't know if the subway tiles should go all the way to the corner without an edge piece, or if we should end with an edge piece. Does that make sense?

Tile just dies into the corner. No bullnose.

Have tile die into the corner. You don't need nothing else.