How can I reduce flex/sway in my pergola?
Triangles are stable, squares are not.
Finish the knee braces.
You might be able to make them more simply by making them from narrower material that will fit between the beam members as they are (ie, they don't need to be the same width as the post, so they can be the same width as the cut-down section of the post the beam is wrapped around.)
Depending on height and why you have double posts on one side, you could also X brace on that side between the double posts.