Ok, first take a breath, this is not as bad as you may think.
What has happened is you left water on your car whilst it baked in the sun. Terry showed us just recently the high pH level of water and unfortunately this just loves to eat japanese clear coat.
How do I know this is rectifiable? I went to a skid pan on sunday last week and my car baked in the sun with concrete water on it. One of the worst.
What I had to do? Take my random orbital buffer and with a lot of sweat I got the marks out. Do you have one? If you dont then find someone with one or go and get a professional detailer to do it.
Clay bar is not going to do shit, yes it has eaten into your clear, but by the pictures, it has not gone all the way through, this is a good thing.
Just never leave your car wet and in the sun. The soap you used would have been a contributing factor. I would imagine that it would be as bad as washing with dishwashing liquid.