Use AWS CloudFormation to config a Simple Websocket server, need manual API Gateway configuration

ws_server.yaml

AWSTemplateFormatVersion: 2010-09-09
Metadata:
  'AWS::CloudFormation::Designer':
    64bc413f-6802-42a9-a2f0-3f88801aef87:
      size:
        width: 60
        height: 60
      position:
        x: 390
        'y': 110
      z: 0
      embeds: []
Resources:
  defaultHandlerRole:
    Type: 'AWS::IAM::Role'
    Properties:
      AssumeRolePolicyDocument:
        Statement:
          - Action: 'sts:AssumeRole'
            Effect: Allow
            Principal:
              Service: lambda.amazonaws.com
        Version: 2012-10-17
      ManagedPolicyArns:
        - !Join 
          - ''
          - - 'arn:'
            - !Ref 'AWS::Partition'
            - ':iam::aws:policy/service-role/AWSLambdaBasicExecutionRole'

  defaultHandlerPolicy:
    Type: 'AWS::IAM::Policy'
    Properties:
      PolicyDocument:
        Statement:
          - Action: 'execute-api:ManageConnections'
            Effect: Allow
            Resource: !Join 
              - ''
              - - 'arn:aws:execute-api:'
                - !Ref 'AWS::Region'
                - ':'
                - !Ref 'AWS::AccountId'
                - ':*/*/POST/@connections/*'
          - Action: 'execute-api:ManageConnections'
            Effect: Allow
            Resource: !Join 
              - ''
              - - 'arn:aws:execute-api:'
                - !Ref 'AWS::Region'
                - ':'
                - !Ref 'AWS::AccountId'
                - ':*/*/GET/@connections/*'
        Version: 2012-10-17
      PolicyName: defaultHandlerPolicy
      Roles:
        - !Ref defaultHandlerRole

  defaultHandler:
    Type: 'AWS::Lambda::Function'
    Properties:
      Code:
        ZipFile: |-
          const AWS = require('aws-sdk');

                exports.handler = async function (event, context) {
                  let connectionInfo;
                  let connectionId = event.requestContext.connectionId;
                
                  const callbackAPI = new AWS.ApiGatewayManagementApi({
                    apiVersion: '2018-11-29',
                    endpoint:
                      event.requestContext.domainName + '/' + event.requestContext.stage,
                  });
                
                  try {
                    connectionInfo = await callbackAPI
                      .getConnection({ ConnectionId: event.requestContext.connectionId })
                      .promise();
                  } catch (e) {
                    console.log(e);
                  }
                
                  connectionInfo.connectionID = connectionId;
                
                  await callbackAPI
                    .postToConnection({
                      ConnectionId: event.requestContext.connectionId,
                      Data:
                        'Use the sendmessage route to send a message. Your info:' +
                        JSON.stringify(connectionInfo),
                    })
                    .promise();
                
                  return {
                    statusCode: 200,
                  };
                };
      Handler: index.handler
      Runtime: nodejs14.x
      Role: !GetAtt defaultHandlerRole.Arn
    DependsOn:
      - defaultHandlerRole
      - defaultHandlerPolicy
    Metadata:
      'AWS::CloudFormation::Designer':
        id: 64bc413f-6802-42a9-a2f0-3f88801aef87