Gap between tub and greenboard
The problem you're likely to have here is different expansion and settle rates for whatever-board-that-is-attached-to-the-tub vs the greenboard behind the vanity. Tiles attached directly to both sides are likely to crack.
You can cut back either side and attach the tile directly to the other side so it covers the gap, caulk with something flexible like 100% silicone.
You could try a very flexible adhesive (possibly modified thinset, but I don't think it's flexible enough) attaching to both sides and hope the flex takes some of the stress out of the joint.
Edit:
If the left surface actually is a tub flange (it doesn't look like it is made from the same fiberglass as the rest of the tub, and there's a mortar in the corner that makes it hard to tell if it's one piece from this photo) - cut the drywall on the right flush with the edge of the vanity (or go behind the vanity if you can) and layer concrete board up to the surface of the flange. Install one large piece that overlaps the flange and is screwed into the studs but not attached to the tub flange. Install tile on the concrete board and caulk silicone along the tile-tub edge.
This assumes the tub has good support and doesn't move much  (1-2mm perhaps) when filled with water and a human.