The stains may be etched into the glass, and thats why you cant remove them. It may be best to replace them.

It is probably etched(glass cancer). I think it may be permanent or very costly to restore.

If it's hard water stains from lime, it can be corrosive. I agree that they may be etched in.

Agree it could be permanent. You might also try equal parts water/vinegar. Spray on, wait 30-40 minutes and rinse. WD-40 could be another option.

I have hard water and my glass is etched on my old shower unit. I added frosted window film on the outside to make it look nice till I had saved up to replace the shower.

I too think it is permanent etching and to avoid that when you get new make sure the shower glass is squeegeed every time the shower is used and clean well once a week.with a vinegar solution

You could add window film on the outside of the doors to hide the spots.

But I have had the best luck with this stuff. My sprinklers sometimes hit the outside of my windows leaving spots and my window cleaner also uses this to remove them. There are other products with the same name, be sure it's this one. Non toxic, easy on hands/skin, smells great and really effective.

Link below:

Bio-clean

If it’s mineral buildup, I’d try white vinegar first. Soak a cloth or paper towels with it, leave them against the affected areas for about 10–15 minutes, then gently clean the glass with a non-scratch pad. For heavier buildup, you may need to repeat it rather than scrub harder.

A small electric scrubber with a soft non-scratch attachment can also save a lot of effort once the deposits have softened. There’s one in this video about 7 cleaning gadgets, along with a few other tools for stubborn cleaning jobs:
https://youtu.be/q9nH48sTjxM

If it is buildup you should be able to find some chemical that can remove it. If it is etched into the glass you would have to replace the door. If you do replace it will suggest that you use a frosted glass to help minimize the impact of the hard water.