When I define this with the new-in-3.10 slots=True argument to dataclass rather than manually defining __slots__ it works just fine. Looks like the pickle format changes rather dramatically to accommodate it.

>>> @dataclass(frozen=True, slots=True)
... class FrozenData:
...     my_string: str
...
>>> deepcopy(FrozenData('initial'))
FrozenData(my_string='initial')

Is there a strong motivation to support manually defined __slots__ on top of slots=True that warrants fixing it for 3.10 onward?