TypeScript error when using `UpdateData<T>` with composite interfaces referencing other interfaces

### Operating System

macOS Sequoia 15.1.1

### Environment (if applicable)

node

### Firebase SDK Version

11.0.2

### Firebase SDK Product(s)

Firestore

### Project Tooling

Vue 3 with Vite

### Detailed Problem Description

TypeScript throws an error when we use `UpdateData` and `T` is an interface that is a combination of other interfaces.

This example **works** because we only have a single `User` interface. It works because the `User` interface does not reference any other interfaces:

```TypeScript
interface User {
age: number;
emotion: {
happy: boolean;
sad: boolean;
};
name: string;
}

const userUpdate: UpdateData = {
age: 30,
"emotion.happy": true,
name: "Alice",
};

const userDocRef = doc(collection(db, "users", "alice"));

await updateDoc(userDocRef, userUpdate);
```

This example **does not work** because we have multiple interfaces that reference each other. Here the `User` interface is referencing the `Emotions` interface, causing the error to show:

```TypeScript
interface Emotions {
happy: boolean;
sad: boolean;
}

interface User {
age: number;
emotion: Emotions; // <-- Notice this change!
name: string;
}

const userUpdate: UpdateData = {
age: 30,
"emotion.happy": true, // <--- Error shows here
name: "Alice",
};

const userDocRef = doc(collection(db, "users", "alice"));

await updateDoc(userDocRef, userUpdate);
```

This is the TypeScript error we see:

> Object literal may only specify known properties, and '"emotion.happy"' does not exist in type '{ age?: number | FieldValue | undefined; emotion?: FieldValue | { happy?: boolean | FieldValue | undefined; sad?: boolean | FieldValue | undefined; } | undefined; name?: string | ... 1 more ... | undefined; }'.ts(2353)

Since types are often built as a composite of other types, it would be good to fix this.

### Steps and code to reproduce issue

Use the code snippets above to see the errors.