The eye is filled with a vitreous humor, the consistency of petroleum jelly.
Floaters are small agglomerations of protein that can form from cells detaching from the retina or any other parts of the eye.
Essentially, small pieces of flotsam and jetsam that are suspended in the viscous material. They don't necessarily float or fall to the bottom.
In a vitrectomy, where the vitreous humor is removed and replaced with a saline solution, the floaters are removed along with the vitreous humor.
Any new floaters that would detach would likely go to the bottom of the eye due to the lower viscosity of the replacement fluid.
Unfortunately, a vitrectomy is almost immediately followed by the formation of cataracts in the lens, so often a lens replacement is done at the same time as the vitrectomy.
My wife had a vitreal detachment occur that leaves "gauze curtains" to appear in her vision--fortunately not in the center 30° of field. This puts her at risk for a retinal detachment
and makes her a good candidate for a vitrectomy + lens replacement. She's waiting until her cataracts progress further.
As for floaters and eye relief, there isn't a relationship.
But, for the visibility thereof, I guess it all depends what you view.
Floaters are most visible on the Moon, often visible on the planets, but almost never visible on other objects.