When the hard water from the irrigation spray collects on the exterior surface of the glass, what I do is wet the surface with soap and water then run a brand new razor blade over the surface to get the majority off. You need to go slow and provide an even amount of force. This will take off the thicker portions. Next spray the surface with Kaboom shower/tile cleaner (or the ZEP equivalent) that has a decalsifier in it. Let this sit for 20-30 secs and keep it wet. Preferably, put up a pop-up tent to keep the glass cool while you are working on it if it is on the ground level. Next I take Cerma-Brite which is a micro pumice infused gel that I get at lowes, which is normally used for cleaning glass surface ranges, and put it on a terry cloth rag. I then put the rag on the bottom of a corner sander and run it over the glass with even pressure, but constantly moving, do not stop in one place. I repeat this process a few times to get as much removed as possible, but it will never be 100%.
Kevin the Window Cleaner (youtube channel) has a few videos about using Glassrenu to fix scratches in glass, you might be able to use the same product and techniques on hard water stains?
If the anything is between the panes, there is nothing you can do about it. You have to replace the window. I have one client that has a full on handprint in the middle of her window in between the glass panes. It came that way from the factory. Since the window is in an unused guest room she didn’t notice it until I cleaned her windows and pointed it out and now we joke that the window was probably made on a Friday at 4:45 and quality control had already headed home for the weekend. That window is over 10 years old at this point and I have yet to come across any remedy.