The interactive REPL is always useful for discovering some of the answers to questions like this:

>>> class Foo(int):
...   __slots__ = 'bar',
...   
Traceback (most recent call last):
  File "<string>", line 1, in <module>
TypeError: nonempty __slots__ not supported for subtype of 'int'
>>> class Foo(str):
...   __slots__ = 'bar',
...
>>>

For your first question, we could possibly change the wording to

• TypeError will be raised if nonempty slots are defined for a class derived from a “variable-length” built-in type such as int, bytes or tuple.

For your second question: I don't know what's being referred to by "variable-length builtin types", so I agree that the wording there is a little opaque.

You can check if any type is variable length or not from python with <type>.__itemsize__ != 0. As for what it means, variable length is a memory layout when data follows the object pointer in single block like tuple in contrast to list which stores items in a separate memory block.

As for what it means, variable length is a memory layout when data follows the object pointer in single block like tuple in contrast to list which stores items in a separate memory block.

Is this definition given anywhere in the documentation? If so, we could maybe link to it from the __slots__ docs here.

Looks like the best place to link to might be https://docs.python.org/3/c-api/typeobj.html#c.PyTypeObject.tp_itemsize. Hardly beginner-friendly, but probably better than no link at all (and I think it's good to keep the section on __slots__ in the datamodel terse).

Yeah, that's the best place I can find too.