Feat: infer parameter types for the implementation signature of an overloaded method

Suggestion

implicitly infer parameter types for the implementation signature of an overloaded method
This issue is a complement to #7763, #34319

🔍 Search Terms

TypeScript interface with multiple signatures;
infer params from different signatures;
implementation signature of an overloaded method;

✅ Viability Checklist

My suggestion meets these guidelines:

• This wouldn't be a breaking change in existing TypeScript/JavaScript code
• This wouldn't change the runtime behavior of existing JavaScript code
• This could be implemented without emitting different JS based on the types of the expressions
• This isn't a runtime feature (e.g. library functionality, non-ECMAScript syntax with JavaScript output, new syntax sugar for JS, etc.)
• This feature would agree with the rest of TypeScript's Design Goals.

⭐ Suggestion

Add an implicit inference to the params or restricted inference in some cases

📃 Motivating Example

Before, you can achieve simple

class Some {
  async request(action: 'auth', payload: AuthPayload): Promise<AuthResponse>
  async request(action: 'pub', payload: PubPayload): Promise<PubResponse>
  async request<S extends Values<SignalingRequests>>(
    ...params: Parameters<S>
  ): Promise<ReturnType<S>> {
    const [action, payload] = params
    switch (action) { /* ... */ }
  }
}
// redundant declarations
// declare Values<T> = T[keyof T]
declare type SignalingRequests = {
  auth: (action: 'auth', payload: AuthPayload) => AuthResponse
  pub: (action: 'pub', payload: PubPayload) => PubResponse
  // ...
}

Now you can use

class Some {
  async request(action: 'auth', payload: AuthPayload): Promise<AuthResponse>
  async request(action: 'pub', payload: PubPayload): Promise<PubResponse>
  async request(...params) {
    if (params[0] == 'auth') {
      const p: AuthPayload = params[1] // this works
    }
    // or you can write:
    const [action, payload] = params
    switch (action) {
      case 'auth':
        payload // AuthPayload
        break
      case 'pub':
        break
      default:
        // exhaustive check
        const nope: never = action
        throw 'nope'
    }
  }
}

💻 Use Cases

Prevent complex type annotation workarounds, simplify codes, make TypeScript sound again!

Best regards.

Start with the motivating overloaded-method examples in this issue, then read the related issues #7763 and #34319. Determine the intended inference rules for implementation parameters and how narrowing should behave across overloads; done means the behavior is specified well enough to guide implementation and tests.