Update dataclass documentation for new __eq__ behavior in 3.13 and add tests

Author: Aniketsy

Doc/library/dataclasses.rst

@@ -105,20 +105,19 @@ Module contents
    - *eq*: If true (the default), an :meth:`~object.__eq__` method will be
      generated.
 
+     This method compares the class by comparing each field in order. Both
+     instances in the comparison must be of the identical type.
+
      .. versionchanged:: 3.13
         The generated ``__eq__`` method now compares each field individually
         (for example, ``self.a == other.a and self.b == other.b``), rather than
         comparing tuples of fields as in previous versions.
 
-     This method compares the class by comparing each field in order. Both
-     instances in the comparison must be of the identical type.
-
      In Python 3.12 and earlier, the comparison was performed by creating
      tuples of the fields and comparing them (for example,
      ``(self.a, self.b) == (other.a, other.b)``).
 
-     If the class already defines :meth:`!__eq__`, this parameter is
-     ignored.
+     If the class already defines :meth:`!__eq__`, this parameter is ignored.
 
    - *order*: If true (the default is ``False``), :meth:`~object.__lt__`,
      :meth:`~object.__le__`, :meth:`~object.__gt__`, and :meth:`~object.__ge__` methods will be