Marks private attributes as read-only with frozen=True

[chbndrhnns]

Describe the bug
PyCharm marks private fields as read-only although pydantic docs say that private attributes are not validated.

Attributes whose name has a leading underscore are not treated as fields by Pydantic, and are not included in the model schema. Instead, these are converted into a "private attribute" which is not validated or even set during calls to init, model_validate, etc.

I am thinking a warning might be useful when trying to modify a frozen model but the red underline might be too much.

To Reproduce

from datetime import datetime
from random import randint

from pydantic import BaseModel, PrivateAttr, ConfigDict


class TimeAwareModel(BaseModel):
    _processed_at: datetime = PrivateAttr(default_factory=datetime.now)
    _secret_value: int

    model_config = ConfigDict(frozen=True)

    @property
    def value(self):
        return self._secret_value

    def __init__(self, **data):
        super().__init__(**data)
        self._secret_value = randint(1, 5)


def test_():
    assert isinstance(TimeAwareModel().value, int)

Expected behavior
Private attributes are excluded from such inspection.

Screenshots

Environments (please complete the following information):

• IDE: Pycharm 2024.2 EAP 6
• OS: [e.g. macOS 12.2.0 ]: macOS
• Pydantic Version [e.g. 1.9.0 ]: 2.8.2
• Plugin version [e.g. 0.3.11 ]: 0.4.14

Additional context
Add any other context about the problem here.