Is there any official documentation of AWS Gateway events sent to Lambda?

This is the closest I've come to an answer, so far. If anyone has more detailed (or general information) I'd gladly take it. In the Lambda documentation you can read that (my emphasis):

The runtime passes three arguments to the handler method. The first argument is the event object, which contains information from the invoker. The invoker passes this information as a JSON-formatted string when it calls Invoke, and the runtime converts it to an object. When an AWS service invokes your function, the event structure varies by service.

Under "Working with other services" in the lambda documentation we only find the examples presented in the question. Instead we can look in the documentation for the service in question, e.g. API Gateway. For API Gateway, under "Working with [HTTP/REST] APIs", you will find descriptions of the event fields for REST and HTTP type APIs.

With that said, the documentation provided still only refer to the described payload structure as "examples". It only provides you with the names of the fields and some basic structure. Data types would have to be inferred from the examples, see the snippets below.

The story seems to be similar for other services you might want to integrate with Lambda like:

• S3
• DynamoDB
• SQS

All that is to be found is examples of payloads, some on the services' own developer's guide other under Lambda's developer's guide.

HTTP v2.0

The following is an example of the payload format for version 2.0 using HTTP type API. For version 1 see the HTTP type integration docs.

{
      version: '2.0',
      routeKey: '$default',
      rawPath: '/my/path',
      rawQueryString: 'parameter1=value1&parameter1=value2&parameter2=value',
      cookies: [ 'cookie1', 'cookie2' ],
      headers: {
        'Header1': 'value1',
        'Header2': 'value2'
      },
      queryStringParameters: { parameter1: 'value1,value2', parameter2: 'value' },
      requestContext: {
        accountId: '123456789012',
        apiId: 'api-id',
        authorizer: { jwt: {
            claims: {'claim1': 'value1', 'claim2': 'value2'},
            scopes: ['scope1', 'scope2']
            }
        },
        domainName: 'id.execute-api.us-east-1.amazonaws.com',
        domainPrefix: 'id',
        http: {
          method: 'POST',
          path: '/my/path',
          protocol: 'HTTP/1.1',
          sourceIp: 'IP',
          userAgent: 'agent'
        },
        requestId: 'id',
        routeKey: '$default',
        stage: '$default',
        time: '12/Mar/2020:19:03:58 +0000',
        timeEpoch: 1583348638390
      },
      body: 'Hello from Lambda',
      pathParameters: {'parameter1': 'value1'},
      isBase64Encoded: false,
      stageVariables: {'stageVariable1': 'value1', 'stageVariable2': 'value2'}
    }

REST v3.0

The following is an example of the payload format for version 3.0 using REST type API. For version 2.0 see the REST type integration docs.

{
   "openapi": "3.0.0",
   "info": {
      "version": "2016-09-12T17:50:37Z",
      "title": "ProxyIntegrationWithLambda"
   },
   "paths": {
      "/{proxy+}": {
         "x-amazon-apigateway-any-method": {
            "parameters": [
               {
                  "name": "proxy",
                  "in": "path",
                  "required": true,
                  "schema": {
                     "type": "string"
                  }
               }
            ],
            "responses": {},
            "x-amazon-apigateway-integration": {
               "responses": {
                  "default": {
                     "statusCode": "200"
                  }
               },
               "uri": "arn:aws:apigateway:us-east-1:lambda:path/2015-03-31/functions/arn:aws:lambda:us-east-1:123456789012:function:SimpleLambda4ProxyResource/invocations",
               "passthroughBehavior": "when_no_match",
               "httpMethod": "POST",
               "cacheNamespace": "roq9wj",
               "cacheKeyParameters": [
                  "method.request.path.proxy"
               ],
               "type": "aws_proxy"
            }
         }
      }
   },
   "servers": [
      {
         "url": "https://gy415nuibc.execute-api.us-east-1.amazonaws.com/{basePath}",
         "variables": {
            "basePath": {
              "default": "/testStage"
            }
         }
      }
   ]
}