Whatever it is you're looking for, this is not it

falsey.py

_hash = 0

class Falsey:
    def __init__(self, *args, **kwargs): pass

    # comparisons
    def __lt__(self, other): return False
    def __le__(self, other): return False
    def __eq__(self, other): return False
    def __ne__(self, other): return False
    def __gt__(self, other): return False
    def __ge__(self, other): return False
    def __not__(self, other): return False

    # representation
    def __bool__(self): return False
    def __str__(self): return ""
    def __repr__(self): return ""
    def __float__(self): return 0.0
    def __len__(self): return 0
    def __contains__(self, other): return False
    def __hash__(self):
        global _hash
        _hash += 1
        return _hash
    def __format__(self, format_spec): return ""
    def __bytes__(self): return b""

    # attribute/item access
    def __getattribute__(self, name): return Falsey()
    def __dir__(self): return ()
    def __getitem__(self, key): return Falsey()
    def __class_getitem__(cls, key): return Falsey()

    # math
    def __add__(self, other): return self
    def __sub__(self, other): return self
    def __mul__(self, other): return self
    def __matmul__(self, other): return self
    def __truediv__(self, other): return self
    def __floordiv__(self, other): return self
    def __mod__(self, other): return self
    def __divmod__(self, other): return self
    def __pow__(self, other, modulo=0): return self
    def __lshift__(self, other): return self
    def __rshift__(self, other): return self
    def __and__(self, other): return self
    def __xor__(self, other): return self
    def __or__(self, other): return self
    def __radd__(self, other): return self
    def __rsub__(self, other): return self
    def __rmul__(self, other): return self
    def __rmatmul__(self, other): return self
    def __rtruediv__(self, other): return self
    def __rfloordiv__(self, other): return self
    def __rmod__(self, other): return self
    def __rdivmod__(self, other): return self
    def __rpow__(self, other, modulo=0): return self
    def __rlshift__(self, other): return self
    def __rrshift__(self, other): return self
    def __rand__(self, other): return self
    def __rxor__(self, other): return self
    def __ror__(self, other): return self
    def __iadd__(self, other): return self
    def __isub__(self, other): return self
    def __imul__(self, other): return self
    def __imatmul__(self, other): return self
    def __itruediv__(self, other): return self
    def __ifloordiv__(self, other): return self
    def __imod__(self, other): return self
    def __ipow__(self, other, modulo=0): return self
    def __ilshift__(self, other): return self
    def __irshift__(self, other): return self
    def __iand__(self, other): return self
    def __ixor__(self, other): return self
    def __ior__(self, other): return self

    # unary math
    def __neg__(self): return 0
    def __pos__(self): return 0
    def __abs__(self): return 0
    def __invert__(self): return 0
    def __round__(self, ndigits=0): return 0
    def __trunc__(self): return 0
    def __floor__(self): return 0
    def __ceil__(self): return 0

    # other
    def __call__(self, *args, **kwargs): return self


if __name__ == "__main__":
    falsey = Falsey()
    assert not falsey
    assert not Falsey[False]
    assert not falsey[falsey]
    assert not falsey(falsey)
    assert not str(falsey)
    assert not int(falsey)
    assert not float(falsey)
    assert not complex(falsey)
    assert not repr(falsey)
    assert not falsey < falsey
    assert not falsey <= falsey
    assert not falsey == falsey
    assert not falsey != falsey
    assert not falsey > falsey
    assert not falsey >= falsey
    assert not falsey in falsey
    assert not hash(falsey) == hash(falsey)
    assert not falsey.false
    assert not falsey + falsey - falsey
    assert not falsey * 2 + 100
    assert not falsey ^ falsey
    assert not falsey ** falsey
    assert falsey is falsey # :(
    assert hasattr(falsey, "false") # :(
    assert not isinstance(falsey, Falsey)

Can definitely be more falsey.