Should operator `|` on `TypedDict` allow for creating intersection-like dicts?

I'm wondering how is the relation between the following PEPs:

• PEP 584 which introduces operator | for dicts, but doesn't mention how it should behave for TypedDict.
• PEP 589 which introduces TypedDict, but doesn't mention the operator |.

According to PEP 589, multiple inheritance can be used to create a combined (or "intersection like") dict, and operator | provides the corresponding behavior at runtime. Thus it would be nice if the type system could handle the combination properly (similar to how it is possible in TypeScript):

from typing import TypedDict

class HasFoo(TypedDict):
    foo: int
    
class HasBar(TypedDict):
    bar: int
    
class HasFooAndBar(HasFoo, HasBar):
    ...
    
def f(a: HasFoo, b: HasBar) -> HasFooAndBar:
    return a | b

From a runtime and type-checking perspective this code looks valid, but currently mypy does not accept it (playground):

main.py:15: error: Incompatible return value type (got "HasFoo", expected "HasFooAndBar")  [return-value]
main.py:15: error: Unsupported operand types for | ("HasFoo" and "HasBar")  [operator]

Pyright seems to have the same behavior.

Apparently operator | can only be used for two instances of the same typed dict, which as far as I can see has limited use cases, because using the operator | on two dicts that already have the same fields is kind of pointless (perhaps it mostly makes sense if the type used total=False).

Possible related discussions and issues I've found:

• https://github.com/python/typing/issues/213 (since this feature for TypedDict probably falls into the "intersection type" category as well?)
• https://github.com/microsoft/pylance-release/issues/2300
• https://github.com/microsoft/pyright/issues/2951

まず PEP 584 と PEP 589 を比較し、次にリンク先の mypy playground で TypedDict の例を再現します。関連する typing、Pylance、Pyright の議論を確認し、提案されている交差型のような動作について合意があるかどうかを判断します。合意されたセマンティクスと、type checker がそれをサポートするための文書化された道筋があれば完了です。