Refactor APIGatewayXXX to eliminate duplicate code

There is an opportunity to DRY by refactoring part of the `APIGateway`, `APIGatewayV2`, and `APIGateway+WebSocket` payload.

As per my assistant:

---
### 1. HTTP Headers and Body Handling
- Properties like `headers`, `multiValueHeaders` (or just `headers` in V2), and `body`, as well as `isBase64Encoded`, appear in all major APIGateway request/response structs:
- `APIGatewayRequest`
- `APIGatewayV2Request`
- `APIGatewayWebSocketRequest`
- Their corresponding response types.

### 2. Context/Identity Structures
- Each request type defines a nested `Context` struct (sometimes with further nesting like `Identity` or `HTTP`), which contains information about the caller, API, stage, request IDs, etc.
- Many fields in these context structs overlap, such as `apiId`, `stage`, `requestId`, `domainName`, and `sourceIp`.

### 3. Codable/Sendable Conformance
- All these types conform to `Codable` (and, where supported, `Sendable`).

### 4. CodingKeys Mapping
- Several structs use custom `CodingKeys` enums to map from JSON input to struct properties, especially for context/requestContext fields.

### 5. Response Struct Pattern
- The response structs (`APIGatewayResponse`, `APIGatewayV2Response`, and by alias, `APIGatewayWebSocketResponse`) all follow a similar pattern: `statusCode`, `headers`, `body`, and `isBase64Encoded`, with slight variations.

---

### Candidates for Code Sharing/Abstraction
- **Protocols:** Define a protocol for common properties (headers, body, isBase64Encoded) and have each struct conform to it.
```swift
protocol APIGatewayRequestCommon: Codable {
var headers: HTTPHeaders? { get }
var body: String? { get }
var isBase64Encoded: Bool? { get }
}
```
- **Shared Context/Identity Structs:** Refactor common context/identity fields into base structs or protocols, and compose them in each specific context struct as needed.
- **Initializers/Decoding Helpers:** Shared extensions or helper initializers to reduce repeated decoding logic for commonly structured properties.

---

**Summary Table of Common Properties:**

| Property | APIGatewayRequest | APIGatewayV2Request | APIGatewayWebSocketRequest |
|------------------|------------------|---------------------|----------------------------|
| headers | ✓ | ✓ | ✓ |
| multiValueHeaders| ✓ | (V2 drops this) | ✓ |
| body | ✓ | ✓ | ✓ |
| isBase64Encoded | ✓ | ✓ | ✓ |
| context/requestContext| ✓ | ✓ | ✓ (as `context`) |
| stage | ✓ (in context) | ✓ (in context) | ✓ (in context) |
| apiId | ✓ (in context) | ✓ (in context) | ✓ (in context) |
| requestId | ✓ (in context) | ✓ (in context) | ✓ (in context) |
| domainName | ✓ (in context) | ✓ (in context) | ✓ (in context) |
| sourceIp | ✓ (in context) | ✓ (in context) | ✓ (in context.identity) |

No source files or tests are named. Start by comparing APIGatewayRequest, APIGatewayV2Request, APIGatewayWebSocketRequest, and their response types, including their nested context structures and CodingKeys. Done means reducing the identified duplication while preserving each event variant's Codable behavior and distinct fields.

Written by the indexing model from the issue text.