Can't pickle a bound method if `getattr(type(im_self), funcname)` fails

Bug report

MWE:

import pickle
import numpy as np
from scipy.interpolate import RectBivariateSpline

class Foo:
    def __init__(self):
        x = np.linspace(0,1,10)[:,None]
        y = np.linspace(2,3,9)[None,:]
        self.f = RectBivariateSpline(x,y,x*y)
        def f2(self,x,y):
            return self.f(x,y)
        self.f2 = f2.__get__(self)

foo = Foo()
pickled = pickle.dumps(foo)
unpickled = pickle.loads(pickled)

print(unpickled.f2(0.5, 0.6))

Expected output is to print [[1.]]. Actually gives an exception

Traceback (most recent call last):
  File ".../pickle-test.py", line 18, in <module>
    unpickled = pickle.loads(pickled)
AttributeError: 'Foo' object has no attribute 'f2'

This issue follows up from the identification an fixing of the same issue with dill, see
https://github.com/uqfoundation/dill/issues/510
https://github.com/uqfoundation/dill/pull/511
where @anivegesana commented

It seems to be a little bit more subtle than that. Because Python 3 implements its own reduce function for methods, I removed it from dill. It turns out that this is not a safe optimization in the case that the func is an inner function. Will be fixed soon.

Your environment

• CPython versions tested on: 3.9.10
• Operating system and architecture: Linux Mint 20.2 on x86-64

Start by reproducing the MWE with pickle.dumps and pickle.loads, focusing on the bound method assigned to Foo.f2 and the reported getattr(type(im_self), funcname) failure. Trace the method round-trip behavior and existing pickle handling; done means the example unpickles successfully and prints [[1.]].