You're right, it would be difficult to do a more traditional larger scarf or a rectangle shape, but some doable options would be:
You'll pretty much need 4 rectangular panels to do a scarf - 1 from each front side, and 2 from the back - so the wrong side of the fabric is not visible. I'm not sure exactly how much length and width you'd be able to squeeze out but you can do some measuring and see if it would be enough. But this would chop up the pattern quite a bit, so if you do want to keep the paisley design, maybe altering it into another garment is a better way to go.
I do like the idea of a beach cover up. You could also go with a tunic/caftan look: hack off the collar. You can make little collar ties that caftans sometimes have, or carve out a V-neck. Cut the sleeves short but not entirely, use the remnants to make a skinny string belt. Or keep the sleeves long, you can chop off the cuffs to give it a more casual vibe, with elastic or without, and set in skinny elastic at the waist. Inspiration:
https://www.brazilianbikinisho.....34333.html
https://kohkoh.fashion/short-s.....k002_a043/
https://www.madewell.com/tie-w.....id=apparel
You could wear that to a beach, or with leggings/skinny jeans in the city.
It's hard to see in the picture, but does it have a button placket, or is the front sewn together?