__hash__ method in str child class causing unintended side effects

Bug report

Consider the following example:

class MyStr(str):
    def __init__(self, value, *args, **kwargs):
        super().__init__(*args, **kwargs)
        self.value = value

    def __hash__(self) -> int:
        return hash(str(self))

    def __str__(self) -> str:
        return str(self.value)

def dummy_func(x):
    class MyClass:
        def __init__(self, data):
            self.data = data
        def __str__(self):
            return self.data
    str(MyClass(x))

dummy_func is a function that should have absolutely no side effects.
However, checkout:

a = MyStr("teststring")
a in {}
# False
dummy_func(a)
a in {}
# Traceback (most recent call last):
#   File "<stdin>", line 1, in <module>
#   File "<stdin>", line 6, in __hash__
#   File "<stdin>", line 6, in __hash__
#   File "<stdin>", line 8, in __str__
#   File "<stdin>", line 8, in __str__
#   File "<stdin>", line 8, in __str__
#   [Previous line repeated 329 more times]
# RecursionError: maximum recursion depth exceeded while calling a Python object
assert id(a.value.data) == id(a)

In this case, dummy_func mutates the input, and creates a weird circular dependency (i.e. id(a.value.data) == id(a)).

The issue can be fixed by removing the __hash__ method of MyStr.

Please confirm the behavior is unintended.

Environment

• CPython versions tested on: Python 3.10.5
• Operating system and architecture: CentOS, x86_64

No source file or test is identified. Start by reproducing the example on CPython 3.10.5 and investigate the interaction between the custom str subclass's hash and str; done would require confirming whether the behavior is unintended and identifying a narrowly scoped regression test or change.