no-private-properties checks only usage of attributes in HTML, not definition of property

no-private-properties rule checks only usage of attributes in HTML, I would like to forbid definition of private/protected properties/attributes. When a property is private it usually should be turned to a state.

This should be an error
```javascript
class Foo extends LitElement {
@property()
__fooProp;
}
```

And it should suggest to make it public or convert to a state
```javascript
class Foo extends LitElement {
@state()
__fooProp;
}
```

I can do the implementation and open a pull request, but would you go by defining a new rule ? (in that case with which name ?) Or by completing existing rule `no-private-properties` to reject definition of private properties too ?

Look at the existing rule 'no-private-properties' in the codebase to understand its current implementation. The issue is about extending this rule to also flag definitions of private properties (e.g., `__fooProp`) in LitElement classes. Check how the rule currently detects usage in HTML and adapt it to also inspect property definitions. The test suite for the rule will show how to verify the new behavior. Running the existing tests and adding new ones for the definition case will confirm the change works.

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