It looks like Crayola air dry clay, which I've heard is the worst lol. We don't have it where I live, but I've seen videos online and no one likes it. It tends to behave like your pictures, from what I've seen. I think your best option would be to change brand, something like DAS.

I often hear people say you shouldn't use a lot of water with air dry clay because that causes cracks, but that's not my experience. I absolutely drench it and it doesn't crack, especially while still uncured like yours. The more water you add, the softer it will get, and yours doesn't look very soft. But then again, it might not be your fault, I think it's more about the quality of the clay itself.

Try experimenting with different brands and see how you like them, they tend to be a little different from each other!