Field of union needs to be different type when reading vs setting

Bug Report

Mypy appears to infer that the type of a field of a variable that is typed as a union is a single type whether that field is being read or updated. The type correct when reading the field (union of the types of the fields) , but not correct when setting as it does not enforce that the value being assigned needs to be valid for both of the types in the union (intersection of the types of the fields).

To Reproduce

class Foo:
    a: int

class Bar:
    a: str

either: Foo | Bar
either.a = 1  # No error, despite not being valid for Bar

More detailed example: https://mypy-play.net/?mypy=latest&python=3.12&gist=bf74f1ba35979f10b1878b2e1abca865

Expected Behavior

Mypy should report the assignment as an error if it does not work with all the types in the union.

Actual Behavior

No error, despite the assignment allowing a field of type str to be an int

Start by running the provided Foo/Bar example and the linked mypy-play reproduction to compare field reads with assignments on a union. Trace the relevant union attribute assignment checking, then confirm the issue is resolved when assignments are accepted only if valid for every union member and the reported example produces an error.