Your quilting so far is beautiful. I think you can do almost anything in the border; the fabric is so busy it is unlikely to show.
On the white background, I’m afraid if you leave it unquilted it will shout “Look at me”, especially if you wash the quilt. Because light colors tend to advance toward the viewer anyway, I would think some simple quilting will help keep the background in the background. Maybe just some straight lines perpendicular to the short side of the rectangles or matchsticks, with spaces between?