Yes, I would tile the wall behind the mirrors.

I would not tile the mirror wall without seeing the entire space. Just like you, I'd like to see how the room came together before deciding. I can see some parts as reflections, but that's not doing it for me.

IMO you need a backsplash but either the whole wall or just to the bottom of the mirrors with tile and for any other ideas we need to see the whole space

How high did you think you would put the tiles on the mirror wall? Please post a further back shot so everyone can assess the situation.

I think vertical tiles are gorgeous. But that’s just the first step. Make sure you have a full plan before buying anything.

I would do a matching backsplash from the countertop material up to the bottom of the mirrors.

Do you still have material left from the countertops? If so, I'd do an 8"-12" splash around the vanity top.

You have an outlet problem on the left side if you want to tile behind the vanity: the outlet would be part on/part off tile.

Wallpaper. Not tile.