Saturn is the least dense planet in the Solar System
Saturn has a density of 0.687 grams/cubic centimeter. Just for comparison, water is 1 g/cm3 and the Earth is 5.52. Since Saturn is less dense than water, it would actually float like an apple if you could find a pool large enough!
Is that an edge-on galaxy on the background or some artifact of the picture taking process?
I would guess it's other satellites. There's a few of those streaks. I don't know where the Earth was relative to JWST and Saturn but even if there weren't some very high orbit satellites in the view, it could be some other Earthly trash in tow. I wouldn't expect random asteroids to be bright enough, but I suppose JWST is plenty sensitive to catch them too. It doesn't have to be big to reflect enough sunlight, just the right angle and position. Satellites are visible from earth all the time
Looks like starlink. Not saying it is, just looks like it.