`--strict-equality` flag not working with membership operator and `Literal` types

Bug Report

When using any container (set, frozenset, list, tuples...) containing Literal based types, the --strict-equality is not detecting any issues when I use the membership operator in a non-overlapping check.

To Reproduce

from typing import Literal

OPTIONS = Literal["a", "b"]
var: list[OPTIONS] = ["a"]
if "c" in var:  # MYPY OK
    pass

Expected Behavior

When the flag --strict-equality is set, I would expect that mypy raises an erorr here. Same as it does when I do a non-overlapping equality check:

from typing import Literal

OPTIONS = Literal["a", "b"]
var: list[OPTIONS] = ["a"]
if var[0] == "c":  #  error: Non-overlapping equality check (left operand type: "Literal['a', 'b']", right operand type: "Literal['c']")  [comparison-overlap]
    pass

Actual Behavior

No errors are raised

Your Environment
Using Mypy version 1.9.0

Start by running the reported Python reproduction with --strict-equality and compare its membership check with the indexed equality check. Locate the strict-equality and membership-analysis entry points, then add a regression test covering a container of Literal values. Done means mypy reports a non-overlapping check for the membership expression without regressing valid membership checks.