My 12.9" 2nd-gen iPad Pro are having these weird stains

The “stains” you see are oils from you fingers - that are adhering to the anti-glare surface of your iPad screen. The oleophobic treatment, designed to reduce finger marks, is a sacrificial coating that does wear-out over time.

Here is Apple’s official guidance as to cleaning Apple devices and accessories - including iPad and its screen:

How to clean your Apple products – Apple Support

If used heavily over that period of time, it is very possible that the surface coating is beginning to deteriorate through use. Similarly, the nature of you handling and cleaning (or lack of cleaning) of the iPad screen will likely impact the lifespan of the oleophobic coating.

Regular and gentle cleaning - coupled with clean hands (avoiding use of creams or other emollient products) will help with keeping the screen clean and free of oil marks. A good quality screen protector is also useful in preserving the original screen finish.