Bleazard
It depends on what kind of seating you would want under the pergola structure. I think you could do a table/chairs for eating or you could do couches/chairs more like a lounge. You could also put a small countertop with some undercounter refrigerators underneath it for easy access to drinks poolside.
Ignore the pergola and ignore the natural stone. What about a slightly raised water feature backdrop for the back edge of the pool like shown here (could be a little taller) and then put landscape screening directly behind it?
Q