feat(apigatewayv2): add missing WebSocketIntegration props (#29566)

### Issue # (if applicable)

None as far as I can tell

### Reason for this change

I was looking at the WebSocket integration to get a feel for #29562, and noticed a couple of missing properties

### Description of changes

* Added support for `timeout` and `contentHandling`
* Minor copy-pasta fixes in documentation and test description

### Description of how you validated changes

I've added unit tests to check these optional properties. I've also updated and verified the following integrations tests:

* `integ.lambda.ts`:
  * `ContentHandlingStrategy` and `TimeoutInMillis` are both correctly set
```sh
$ aws apigatewayv2 get-integration --api-id bu24s9i8t0 --integration-id fxqec8c
{
    "ConnectionType": "INTERNET",
    "ContentHandlingStrategy": "CONVERT_TO_TEXT",
    "IntegrationId": "fxqec8c",
    "IntegrationMethod": "POST",
    "IntegrationType": "AWS_PROXY",
    "IntegrationUri": "arn:aws:apigateway:us-east-1:lambda:path/2015-03-31/functions/arn:aws:lambda:us-east-1:637423343434:function:WebSocketApiInteg-DefaultHandler604DF7AC-GSQYxsiaKjkz/invocations",
    "PassthroughBehavior": "WHEN_NO_MATCH",
    "PayloadFormatVersion": "1.0",
    "RequestTemplates": {},
    "TimeoutInMillis": 10000
}
```
* `integ.aws.ts`:
  * `ContentHandlingStrategy`, `TemplateSelectionExpression`, `TimeoutInMillis`,  `PassthroughBehavior`, and `RequestParameters` are all correctly set
 
```sh
$ aws apigatewayv2 get-integration --api-id qp17tw07w3 --integration-id hycmjxb
{
    "ConnectionType": "INTERNET",
    "ContentHandlingStrategy": "CONVERT_TO_BINARY",
    "CredentialsArn": "arn:aws:iam::637423343434:role/integ-aws-websocket-integrat-ApiGatewayRoleD2518903-i80lztfxo5XI",
    "IntegrationId": "hycmjxb",
    "IntegrationMethod": "POST",
    "IntegrationResponseSelectionExpression": "${integration.response.statuscode}",
    "IntegrationType": "AWS",
    "IntegrationUri": "arn:aws:apigateway:us-east-1:dynamodb:action/PutItem",
    "PassthroughBehavior": "WHEN_NO_TEMPLATES",
    "PayloadFormatVersion": "1.0",
    "RequestParameters": {
        "integration.request.header.Content-Type": "'application/x-www-form-urlencoded'"
    },
    "RequestTemplates": {
        "application/json": "{\"TableName\":\"MyTable\",\"Item\":{\"id\":{\"S\":\"$context.requestId\"}}}"
    },
    "TemplateSelectionExpression": "\\$default",
    "TimeoutInMillis": 10000
}
```

### Checklist
- [x] My code adheres to the [CONTRIBUTING GUIDE](https://github.com/aws/aws-cdk/blob/main/CONTRIBUTING.md) and [DESIGN GUIDELINES](https://github.com/aws/aws-cdk/blob/main/docs/DESIGN_GUIDELINES.md)

----

*By submitting this pull request, I confirm that my contribution is made under the terms of the Apache-2.0 license*

packages/@aws-cdk-testing/framework-integ/test/aws-apigatewayv2-integrations/test/websocket/integ.aws.js.snapshot/integ-aws-websocket-integration.template.json

@@ -97,6 +97,7 @@
     "ApiId": {
      "Ref": "mywsapi32E6CE11"
     },
+    "ContentHandlingStrategy": "CONVERT_TO_BINARY",
     "CredentialsArn": {
      "Fn::GetAtt": [
       "ApiGatewayRoleD2518903",
@@ -117,6 +118,10 @@
       ]
      ]
     },
+    "PassthroughBehavior": "WHEN_NO_TEMPLATES",
+    "RequestParameters": {
+     "integration.request.header.Content-Type": "'application/x-www-form-urlencoded'"
+    },
     "RequestTemplates": {
      "application/json": {
       "Fn::Join": [
@@ -130,7 +135,9 @@
        ]
       ]
      }
-    }
+    },
+    "TemplateSelectionExpression": "\\$default",
+    "TimeoutInMillis": 10000
    }
   },
   "mywsapiconnectRoute45A0ED6A": {

packages/@aws-cdk-testing/framework-integ/test/aws-apigatewayv2-integrations/test/websocket/integ.aws.ts

@@ -1,7 +1,7 @@
-import { HttpMethod, WebSocketApi, WebSocketStage } from 'aws-cdk-lib/aws-apigatewayv2';
+import { ContentHandling, HttpMethod, PassthroughBehavior, WebSocketApi, WebSocketStage } from 'aws-cdk-lib/aws-apigatewayv2';
 import * as dynamodb from 'aws-cdk-lib/aws-dynamodb';
 import * as iam from 'aws-cdk-lib/aws-iam';
-import { App, RemovalPolicy, Stack } from 'aws-cdk-lib';
+import { App, Duration, RemovalPolicy, Stack } from 'aws-cdk-lib';
 import { WebSocketAwsIntegration, WebSocketMockIntegration } from 'aws-cdk-lib/aws-apigatewayv2-integrations';
 import { IntegTest } from '@aws-cdk/integ-tests-alpha';
 
@@ -42,6 +42,9 @@ webSocketApi.addRoute('$connect', {
     integrationUri: `arn:aws:apigateway:${stack.region}:dynamodb:action/PutItem`,
     integrationMethod: HttpMethod.POST,
     credentialsRole: apiRole,
+    requestParameters: {
+      'integration.request.header.Content-Type': '\'application/x-www-form-urlencoded\'',
+    },
     requestTemplates: {
       'application/json': JSON.stringify({
         TableName: table.tableName,
@@ -52,6 +55,10 @@ webSocketApi.addRoute('$connect', {
         },
       }),
     },
+    templateSelectionExpression: '\\$default',
+    passthroughBehavior: PassthroughBehavior.WHEN_NO_TEMPLATES,
+    contentHandling: ContentHandling.CONVERT_TO_BINARY,
+    timeout: Duration.seconds(10),
   }),
 });
 

packages/@aws-cdk-testing/framework-integ/test/aws-apigatewayv2-integrations/test/websocket/integ.lambda.js.snapshot/WebSocketApiInteg.template.json

@@ -431,6 +431,7 @@
     "ApiId": {
      "Ref": "mywsapi32E6CE11"
     },
+    "ContentHandlingStrategy": "CONVERT_TO_TEXT",
     "IntegrationType": "AWS_PROXY",
     "IntegrationUri": {
      "Fn::Join": [
@@ -454,7 +455,8 @@
        "/invocations"
       ]
      ]
-    }
+    },
+    "TimeoutInMillis": 10000
    }
   },
   "mywsapidefaultRouteE9382DF8": {