Fix missing type store for overloads (#16803)

Add missing call to store inferred types if an overload match is found
early. All other code paths already do that.


### Some background on the issue this fixes
I recently saw an interesting pattern in `aiohttp` to type values in an
`dict[str, Any]` by subclassing dict.

```py
T = TypeVar("T")
U = TypeVar("U")

class Key(Generic[T]):
    ...

class CustomDict(dict[Key[Any] | str, Any]):
    @overload  # type: ignore[override]
    def get(self, __key: Key[T]) -> T | None:
        ...

    @overload
    def get(self, __key: Key[T], __default: U) -> T | U:
        ...

    @overload
    def get(self, __key: str) -> Any | None:
        ...

    @overload
    def get(self, __key: str, __default: Any) -> Any:
        ...

    def get(self, __key: Key[Any] | str, __default: Any = None) -> Any:
        """Forward to super implementation."""
        return super().get(__key, __default)

    # overloads for __getitem__, setdefault, pop
    # ...

    @overload  # type: ignore[override]
    def __setitem__(self, key: Key[T], value: T) -> None:
        ...

    @overload
    def __setitem__(self, key: str, value: Any) -> None:
        ...

    def __setitem__(self, key: Key[Any] | str, value: Any) -> None:
        """Forward to super implementation."""
        return super().__setitem__(key, value)
```

With the exception that these overloads aren't technically compatible
with the supertype, they do the job.
```py
d = CustomDict()
key = Key[int]()
other_key = "other"
assert_type(d.get(key), int | None)
assert_type(d.get("other"), Any | None)
```

The issue exists for the `__setitem__` case. Without this PR the
following would create an issue. Here `var` would be inferred as
`dict[Never, Never]`, even though it should be `dict[Any, Any]` which is
the case for non-subclassed dicts.
```py
def a2(d: CustomDict) -> None:
    if (var := d.get("arg")) is None:
        var = d["arg"] = {}
        reveal_type(var)
```

mypy/checkexpr.py

@@ -2825,6 +2825,7 @@ def infer_overload_return_type(
                 # Return early if possible; otherwise record info, so we can
                 # check for ambiguity due to 'Any' below.
                 if not args_contain_any:
+                    self.chk.store_types(m)
                     return ret_type, infer_type
                 p_infer_type = get_proper_type(infer_type)
                 if isinstance(p_infer_type, CallableType):

test-data/unit/check-generics.test

@@ -1480,6 +1480,30 @@ if int():
     b = f(b)
 [builtins fixtures/list.pyi]
 
+[case testGenericDictWithOverload]
+from typing import Dict, Generic, TypeVar, Any, overload
+T = TypeVar("T")
+
+class Key(Generic[T]): ...
+class CustomDict(dict):
+    @overload  # type: ignore[override]
+    def __setitem__(self, key: Key[T], value: T) -> None: ...
+    @overload
+    def __setitem__(self, key: str, value: Any) -> None: ...
+    def __setitem__(self, key, value):
+        return super().__setitem__(key, value)
+
+def a1(d: Dict[str, Any]) -> None:
+    if (var := d.get("arg")) is None:
+        var = d["arg"] = {}
+        reveal_type(var)  # N: Revealed type is "builtins.dict[Any, Any]"
+
+def a2(d: CustomDict) -> None:
+    if (var := d.get("arg")) is None:
+        var = d["arg"] = {}
+        reveal_type(var)  # N: Revealed type is "builtins.dict[Any, Any]"
+[builtins fixtures/dict.pyi]
+
 
 -- Type variable scoping
 -- ---------------------

test-data/unit/typexport-basic.test

@@ -1236,6 +1236,27 @@ LambdaExpr(10) : def (x: builtins.int) -> builtins.int
 LambdaExpr(12) : def (y: builtins.str) -> builtins.str
 LambdaExpr(13) : def (x: builtins.str) -> builtins.str
 
+[case testExportOverloadArgTypeDict]
+## DictExpr
+from typing import TypeVar, Generic, Any, overload, Dict
+T = TypeVar("T")
+class Key(Generic[T]): ...
+@overload
+def f(x: Key[T], y: T) -> T: ...
+@overload
+def f(x: int, y: Any) -> Any: ...
+def f(x, y): ...
+d: Dict = {}
+d.get(
+  "", {})
+f(
+  2, {})
+[builtins fixtures/dict.pyi]
+[out]
+DictExpr(10) : builtins.dict[Any, Any]
+DictExpr(12) : builtins.dict[Any, Any]
+DictExpr(14) : builtins.dict[Any, Any]
+
 -- TODO
 --
 -- test expressions