ApiGatewayManagementApi - InvalidSignatureException - Credential should be scoped to correct service: 'execute-api'

[samstradling]

Describe the bug
When running the ApiGatewayManagementApi I get the following error:

(node:44809) UnhandledPromiseRejectionWarning: InvalidSignatureException: Credential should be scoped to correct service: 'execute-api'. 
    at deserializeAws_restJson1PostToConnectionCommandError (<project_root>/node_modules/@aws-sdk/client-apigatewaymanagementapi/dist/cjs/protocols/Aws_restJson1.js:287:41)
    ...

The signingService is currently set to apigateway rather than execute-api.

aws-sdk-js-v3/clients/client-apigatewaymanagementapi/endpoints.ts

Line 82 in 64d2210

return Promise.resolve({ signingService: "apigateway", ...regionInfo });

Since this is used in SigV4 it results in it being invalid:
https://docs.aws.amazon.com/general/latest/gr/sigv4_signing.html

SDK version number
3.0.0

Is the issue in the browser/Node.js/ReactNative?
node.js

Details of the browser/Node.js/ReactNative version

$ node -v
v12.16.1

To Reproduce (observed behavior)

const {
  PostToConnectionCommand,
  ApiGatewayManagementApiClient,
} = require('@aws-sdk/client-apigatewaymanagementapi');

const API_ID = '';
const REGION = '';
const STAGE = '';
const CONNECTION_ID = '';

const apiGatewayManagementApiClient = new ApiGatewayManagementApiClient({
  endpoint: `https://${API_ID}.execute-api.${REGION}.amazonaws.com/${STAGE}`,
});

(async () => {
  const command = new PostToConnectionCommand({
    ConnectionId: CONNECTION_ID,
    Data: new TextEncoder().encode('test-message'),
  })

  const res = await apiGatewayManagementApiClient.send(command);
  console.log(res);
})();

Expected behavior
The request is signed with execute-api as the service.

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