`functools.partial` plugin is only triggered on calls

Bug Report

partial support is too fragile and easy to fool.

To Reproduce

import typing as t
from functools import partial

# 1.
# uncomment this to get type error
# partial(lambda x, y: x + y, 10)()

# 2.
# But this silly little thing passes type-check
silly: t.Callable[[], int] = partial(lambda x, y: x + y, 10)
silly()

Expected Behavior

Fail to coerce partial into incompatible callable type.

Actual Behavior

Success: no issues found in 1 source file

Your Environment

• Mypy version used: master
• Mypy command-line flags: no
• Mypy configuration options from mypy.ini (and other config files):
• Python version used: 3.12

Looks like we carry information about needed arguments somewhere anyways, since 1 fails type check due to not enough arguments, so why we allow to coerce that partial into incompatible callable?
Perhaps this is due to this definition of partial:

    def __call__(self, /, *args: Any, **kwargs: Any) -> _T: ...

But, for example, pyright takes that into account and fails as expected:

[nix-shell:/tmp]$ pyright issue.py
/tmp/issue.py
  /tmp/issue.py:10:30 - error: Expression of type "partial[Unknown]" is incompatible with declared type "() -> int"
    Type "partial[Unknown]" is incompatible with type "() -> int"
      Extra parameter "y" (reportAssignmentType)
1 error, 0 warnings, 0 informations

I think it worth fixing, since we support partial and it is useful to rely on that support. It can be fixed, for example, as viewing partial result internally not as partial[int] type, but as something like

class FakePartial(Protocol[P, Ret]):
    @property
    def args(self) -> tuple[Any, ...]: ...
    
    @property
    def keywords(self) -> dict[any, ...]: ...

    @property
    def func(self) -> t.Callable[..., Ret]: ...

    def __call__(self, *args: P.args, **kwargs: P.kwargs) -> Ret: ...

Python 3.12 と mypy master を使って 2 つの例を再現し、その後、issue にリンクされている typeshed functools.pyi の定義と動作を比較します。既存の functools.partial のサポートと、その引数情報を追跡します。引数を取らない callable への互換性のない代入が拒否され、有効な partial 呼び出しは引き続き型チェックを通過すれば完了です。