Incompatible types in assignment when a with block has inner method

Bug Report

mypy reports an Incompatible types in assignment error when the variable name defined is same across "with" blocks and any of the "with" block contain an inner method. I hope this is on the lines of #15605 and a possible variant of #12246.

To Reproduce

Please use the below code:

with open('file1', 'r') as f:
    def do_something(x: int, y: int) -> int:
        return x + y
    
    do_something(2, 3)

with open('file2', 'rb') as f:
    pass

Expected Behavior

Type check passes.

Actual Behavior

I observed the following error:

main.py:7: error: Incompatible types in assignment (expression has type "BufferedReader", variable has type "TextIOWrapper") [assignment]

Your Environment

• Mypy version used: 1.6.1
• Mypy command-line flags: None, just ran mypy main.py
• Mypy configuration options from mypy.ini (and other config files): None
• Python version used: 3.9.13

Start by running mypy main.py with the reproduced nested-method and repeated-with-variable example, using the reported mypy 1.6.1 behavior as a baseline. Trace how assignment types are inferred across with blocks containing inner methods; done means the example type-checks without the incompatible-assignment error and the behavior is covered by an appropriate regression test.