Incompatible types in assignment (expression has type "bool", variable has type "Literal[False]") with nested code

To Reproduce

class Bar:
    def __init__(self, baz: bool) -> None:
        self.baz: bool = baz


def busted(key: int, bar: Bar) -> None:
    b = bar
    if key > 1:
        if b.baz: # No error without this block
            return
        if key != 1:
            baz = b.baz
    if key > 0:
        if key < 5:
            baz = b.baz  # error: Incompatible types in assignment (expression has type "bool", variable has type "Literal[False]")

Expected Behavior
This silly example is the smallest I could trim my real code to. It is a lot of nested if that stores references to bool properties in various levels of nesting. At no point is anything else assigned to the local variable (baz in this example).

Actual Behavior
error: Incompatible types in assignment (expression has type "bool", variable has type "Literal[False]")

Your Environment
mypy --version
mypy 0.981 (compiled: yes)
python --version
Python 3.10.6
Mypy command-line flags: None

Start by running the provided nested-if reproduction with mypy 0.981 on Python 3.10.6 and confirm the Literal[False] assignment error. Trace how the checker infers the type of baz across the conditional branches. Done means the valid bool assignment no longer produces this diagnostic, with regression coverage for the example.