Common glass absorbs most of the UV light, and your lens and cornea absorb the rest. If UV light did hit your retina, you'd actually notice it - people who lack a cornea and/or lens can actually notice UV light, which is why artificial lenses like you'd get after in cataract surgery are now made of UV-absorbant materials.

So unless you have a rare medical condition AND you're buying plastic lens glasses, I think you're worrying for nothing.

All that is true except almost no sunglasses made with the glass lenses. It’s almost all plastic with UV shielding layer.