int x = 10;
I think the text mentioning "pointer to object type" is talking about the type representing a "pointer to object", i.e. a pointer to something.
Does this mean that the object where 10 is stored saves information about the type of value stored in the object
Type information of variables that you declare in C is relevant only during the process of compiling your program. Once your program has been compiled, type information is gone. There is no type information to store in memory at runtime.
Here is one place where C99 standard mentions "pointer to object type":
22.214.171.124 Array subscripting
One of the expressions shall have type "pointer to object type", the other expression shall have integer type, and the result has type "type"
What this means is that the pointer expression has to be a pointer to data object of a specific type. It cannot be a pointer to function, or a pointer to data with no specific type (i.e.