I am an interior designer and artist and I have so many art pieces with vibrant colors just like yours. The painting is absolutely beautiful and It will be your focal point in the place. If you chose rugs with patterns like the ones you shared the color balance and theme will be confusing to the eye. And your eyes won’t have any space to relax and go back to the focal point in the space which is your art again. You need resting points such as a carpet with muted colors and no patterns.

I think going with an over dyed rug may be a good compromise. you still get the color, but not the busy pattern

Pick one or two of the art color, and bring in the rug to match.

the burgundy/violet one on the far right has multiple shades, but they're very discreet. it plays w/the artwork well, but doesn't compete w/it.

same w/this one

You want something in the Red/Violet range of colors (if going w/the purple theme)

all 3 of these are red-violets.

if you want to go the blue / green route, then go w/that shade. accent w/the other colors

if you wanted to use the rugs you picked, then everything else in that room would need to be very similar and solid. otherwise, it would be a circus. also too, if the rug/art are in close proximity, then let one be the star. If the art is across the room from the rug, you can do something a bit busier. But the other items in the room are playing back-up only. just keep that in mind.

dusty lavenders are pretty too

All those rugs have too much large pattern to work with the artwork. Since the art has such large patterns you want contrast. The rug should be solid, striped, or with a very small pattern so it doesn't compete with the art. You can choose a vibrant solid color from the art for the rug, which could look wonderful. Add some extra pattern in your pillows.

Thank you all so much. I do love the rugs I posted but knew in my gut I needed something simpler. You've convinced me! Happy New Year to you all - be healthy and well.