apigatewayv2: stateMachineArn does not fit schema for Operation: StepFunctions-StartSyncExecution

### Describe the bug

I'm trying to create a ApiGatewayV2 route with AWS StepFunction integration. For this I'm using the L1 constructs but getting the following error message:

```shell
UPDATE_ROLLBACK_COMPLETE: Parameter: stateMachineArn does not fit schema for Operation: StepFunctions-StartSyncExecution. (Service: AmazonApiGatewayV2; Status Code: 400; Error Code: BadRequestException
```

### Expected Behavior

The creation of the ApiGatewayV2 route with an AWS StepFunction integration

### Current Behavior

Stack deployment failure and rollbacked:

```shell
UPDATE_ROLLBACK_COMPLETE: Parameter: stateMachineArn does not fit schema for Operation: StepFunctions-StartSyncExecution. (Service: AmazonApiGatewayV2; Status Code: 400; Error Code: BadRequestException
```

### Reproduction Steps

```typescript
const demoStateMachine = new StateMachine(scope, 'DemoStateMachine', {
stateMachineType: StateMachineType.EXPRESS,
definitionBody:
DefinitionBody.fromChainable(
new Pass(scope, 'PassState')
),
});

const role = new Role(scope, 'DemoStateMachineRole', {
assumedBy: new ServicePrincipal('apigateway.amazonaws.com'),
});

const integration = new CfnIntegration(
this.scope,
"DemoStateMachineIntegration",
{
apiId: gateway.httpApiId,
integrationType: HttpIntegrationType.AWS_PROXY,
integrationSubtype: 'StepFunctions-StartSyncExecution',
credentialsArn: role.roleArn,
payloadFormatVersion: PayloadFormatVersion.VERSION_1_0.version,
requestParameters: {
stateMachineArn: demoStateMachine.stateMachineArn
}
}
);

new CfnRoute(this.scope, 'CheckoutRoute', {
apiId: gateway.httpApiId,
routeKey: `${HttpMethod.POST} demo`,
authorizationType: 'NONE',
target: `integrations/${integration.ref}`,
});

```

### Possible Solution

_No response_

### Additional Information/Context

_No response_

### CDK CLI Version

2.85.0

### Framework Version

2.85.0

### Node.js Version

16.18.0

### OS

macOS 13.4.1

### Language

Typescript

### Language Version

4.9.5

### Other information

_No response_

Start by reproducing the shown TypeScript configuration using CfnIntegration and CfnRoute, focusing on requestParameters for StepFunctions-StartSyncExecution. Investigate why stateMachineArn is rejected during deployment; done means the stack deploys successfully and creates the ApiGatewayV2 route with the Step Functions integration.

Written by the indexing model from the issue text.