Missing type error for invalid use of #private field

Bug Report

ES #private fields are not source-positional, but scoped to each instance of a class. (That is unfortunate, in my humble opinion). However TypeScript is not detecting this case.

🔎 Search Terms

typescript no type error private field mixin

🕗 Version & Regression Information

4.3-beta (I didn't try earlier)

⏯ Playground Link

Playground link with relevant code

💻 Code

type Ctor<T = {}> = new (...args: any[]) => T

function FooMixin<C extends Ctor>(Base: C) {
  return class Foo extends Base {
    #foo = 123
    test(foo: Foo) {
      console.log(foo.#foo)
    }
  }
}

class Cat extends FooMixin(Object) {}
class Dog extends FooMixin(Object) {}

const c = new Cat
c.test(new Dog) // Should there be a type error here, perhaps?

🙁 Actual behavior

No type error, but only a runtime error.

🙂 Expected behavior

There should perhaps also be a type error, if that's possible.

Mixin docs

The TypeScript Mixin documentation advertises that people can use #private fields with class-factory mixins:

// Mixins may not declare private/protected properties
// however, you can use ES2020 private fields

This may lead people to the try them and they'll have this issue.

Start with the linked TypeScript Playground and reproduce the mixin example involving #private fields, FooMixin, Cat, and Dog. Read the type-checking behavior around private-field identity and determine what diagnostic, if any, should be produced for c.test(new Dog); done requires an agreed semantic and corresponding regression coverage.