Nit: Inside the city of Zürich there are 4 public baths _in Limmat_ (and 5 more in the lake from which the river flows). https://badi-info.ch doesn't mention any baths on Limmar outside of the city (though there surely are unofficial beaches there and there's lots of people floating downriver on inflatable unicorns in the summer).
BTW. Swimming in the spot depicted on the photo is usually forbidden (due to existence of boat traffic and various places where collisions would be hard to sufficiently surely avoid); the photo was taken during a once-a-year event that involves forbidding boat traffic from using that part of the river for a change.