fix(aws-lambda): add jwt and lambda authorizer types for API Gateway v2 - #5142

Problem

ApiGatewayRequestContextV2["authorizer"] declares only the iam variant:

interface Authorizer {
  iam?: {
    accessKey: string
    accountId: string
    // ...
  }
}

API Gateway populates two other keys on that object, so reading either one is a
TypeScript error even though the value is present at runtime:

app.use(async (ctx, next) => {
  ctx.set('userId', ctx.env.event.requestContext.authorizer.lambda.userId)
  //                                                          ^^^^^^
  // error TS2339: Property 'lambda' does not exist on type 'Authorizer'.
})

This affects anyone using an HTTP API (payload format 2.0) with a Lambda
(REQUEST) authorizer or a JWT authorizer. ApiGatewayRequestContextV2 is
exported from hono/aws-lambda, so the gap is user-facing. The reported
workaround is to redeclare the type by hand before using the bindings.

Why these two keys

• jwt — AWS's own payload format 2.0 example carries
  requestContext.authorizer.jwt with claims and scopes:
  https://docs.aws.amazon.com/apigateway/latest/developerguide/http-api-develop-integrations-lambda.html
• lambda — a Lambda authorizer returns an optional context object
  (simple response or IAM policy response), which API Gateway delivers to the
  integration under requestContext.authorizer.lambda:
  https://docs.aws.amazon.com/apigateway/latest/developerguide/http-api-lambda-authorizer.html

The shapes mirror @types/aws-lambda
(APIGatewayEventRequestContextJWTAuthorizer and
APIGatewayEventRequestContextLambdaAuthorizer), which the issue cites as the
reference. lambda is typed Record<string, unknown> | null rather than
generic to keep the change contained; null is what API Gateway sends when the
authorizer returns no context. scopes is string[] | null because a JWT with
no scope claim yields null.

Changes

interface Authorizer {
  iam?: { /* unchanged */ }
  jwt?: {
    claims: Record<string, string | number | boolean | string[]>
    scopes: string[] | null
  }
  /**
   * The `context` object returned by a Lambda (REQUEST) authorizer.
   * It is `null` when the authorizer returns no context.
   */
  lambda?: Record<string, unknown> | null
}

Both properties are optional and iam is untouched, so this is purely additive
and backwards compatible. Types only — no runtime change.

Tests

Added a V2 request context authorizer block to
src/adapter/aws-lambda/handler.test.ts covering both authorizer variants
end-to-end through handle(), plus an expectTypeOf check that each variant is
optional and that scopes accepts null.

Without the type change these fail tsc -p tsconfig.spec.json with exactly the
error from the issue:

error TS2339: Property 'lambda' does not exist on type 'Authorizer'.
error TS2339: Property 'jwt' does not exist on type 'Authorizer'.

bun run test passes: 145 files, 4619 tests. eslint and prettier --check
are clean on the changed files.

Closes #3281

The author should do the following, if applicable

• Add tests
• Run tests
• bun run format:fix && bun run lint:fix to format the code
• Add TSDoc/JSDoc to document the code