How can I clean severe water stains from shower screen glass?

Sounds like hard water stains...Fill a spray bottle with a 50/50 solution of Dawn dish soap and vinegar. Spray it on the hard water stains and let it work. If they are tougher stains, you may have to scrub with a plastic scrubbie!

Try 91-proof rubbing alcohol and non-scratch scrubbing pad, and ventilation while applying.

Have you tried CLR?

Try rubbing alcohol!

Cut a grapefruit in half, cover with kosher salt and use as a scrubber.

Lysol Power Scum cleaner in the blue trigger spray bottle with a Magic Eraser or a scrub brush.

Wet & forget shower for a slower, no scrub solution. You can use 2x a week to accelerate the cleaning process then once a week to keep it clean.

I clean professionally and this is what I do. Get a good soap scum remover such as scrubbing bubbles or lysol power bath. Spray it on, let sit for several minutes and then use a nylon scrubby to gently scrub the glass. Rinse. Repeat immediately after the first time if you still have soap scum on the glass. Once you do this deep clean, you shouldn't need to scrub it. Simply spray the glass weekly with the soap scum remover and let sit, rinse.