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

Start by comparing PEP 584 and PEP 589, then reproduce the TypedDict example in the linked mypy playground. Review the related typing, Pylance, and Pyright discussions to determine whether the proposed intersection-like behavior has consensus. Done would require an agreed semantic and a documented path for type checkers to support it.