The best way to clean toilet bowl stains

If the problem is mineral clogging of the under-rim channels on the toilet, and this does produce the symptoms you describe, then neither CLR no vinegar may be enough to clear up the blockage. The traditional treatment is a cup or two of muriatic acid (HCl 36%, from the hardware store) down the overflow hole in the tank. That goes directly to the rim vents. Pour the stuff in, wait an hour, and flush. Gloves and eye protection are recommmended, and a funnel so as to avoid spillage and corroding the metal parts in your tank. This looks like decent writeup of the method: How to Fix a Slow Toilet

It's essentially an external kidney stone.

You can use various types of acid - sometimes a alternating approach of chlorine bleach (by itself) to kill the biofilm that's exposed and acid (by itself) to remove the "more or less limestone" is beneficial. The biofilm can prevent or slow the acid from getting to the underlying stony material, and it tends to have a layered structure.

Vinegar works, but slowly. Citric acid should work better (it's a stronger acid) but can be harder to find. Muriatic (aka hydrochloric) makes me a bit uncomfortable, personally, but there are commercial toilet cleaners that contain it. Be sure to use gloves and goggles if you opt for the stronger stuff.