Noticing eye floaters three months after surgery under general anesthesia. Can drugs used for anesthesia cause eye problems such as floaters?

No. Commonly used drugs for anesthesia do not directly cause eye floaters. You should see an eye doctor as soon as possible if you notice a sudden increase in floaters, eye pain, changes in vision.
Not related. You most probably have a vitreous floater. The clear gel that fills eyeball is normally attached to all parts of the inside of the eye. As we get older it can become more liquid (watery) and detaches from the back of the retina causing your "dirt" floater. This can also reult in a retinal tear or detachment you should see your eye doctor to check the retina for this or hemorrhage (blood).