### Is there an existing issue for this?

- [X] I have searched the existing issues

### Current Behavior

VTL template for request is not properly processed. 

Testing with sample project provided at https://github.com/localstack/localstack-terraform-samples/tree/master/apigateway-lambda-velocity several parameters of the request, such as path and identity are not properly parsed. 

For a request like this:

```
curl -X POST "0naclskncu.execute-api.localhost.localstack.cloud:4566/local/test" -H 'content-type: application/json' -d '{ "greeter": "cesar" }'
```

the result is:
```
{
"body": {"greeter": "cesar"},
"method": "POST",
"principalId": "",
"stage": "local",

"cognitoPoolClaims" : {

"sub": ""
},

"enhancedAuthContext":     {
}
,

"headers":     {
}
,

"query":     {
}
,

"path":     {

""proxy"":
""test""
}
,

"identity":     {

""accountId"":
"0"
,
""sourceIp"":
""172.17.0.1""
,
""userAgent"":
""curl/7.84.0""
}
,

"stageVariables":     {
}
,

"requestPath": "/{proxy+}"
}
```
Notice the extra double quotes on path and identity values which results in a non valid JSON document.

From the localstack logs:

```
botocore.errorfactory.UnsupportedMediaTypeException: An error occurred (UnsupportedMediaTypeException) when calling the Invoke operation: The payload is not JSON:


{
"body": {"greeter": "cesar"},
"method": "POST",
"principalId": "",
"stage": "local",

"cognitoPoolClaims" : {

"sub": ""
},

"enhancedAuthContext":     {
}
,

"headers":     {
}
,

"query":     {
}
,

"path":     {

""proxy"":
""test""
}
,

"identity":     {

""accountId"":
"0"
,
""sourceIp"":
""172.17.0.1""
,
""userAgent"":
""curl/7.84.0""
}
,

"stageVariables":     {
}
,

"requestPath": "/{proxy+}"
}

2022-11-16T09:47:17.833  INFO --- [   asgi_gw_0] localstack.request.http    : POST /local/test => 400; Request(b'{ "greeter": "cesar" }', headers={'Host': '0naclskncu.execute-api.localhost.localstack.cloud:4566', 'User-Agent': 'curl/7.84.0', 'Accept': '*/*', 'content-type': 'application/json', 'Content-Length': '22', 'x-localstack-tgt-api': 'apigateway'}); Response(b'{"Type": "User", "message": "Error invoking integration for API Gateway ID \'0naclskncu\': An error occurred (UnsupportedMediaTypeException) when calling the Invoke operation: The payload is not JSON:  \\n\\n  \\n  {\\n    \\"body\\": {\\"greeter\\": \\"cesar\\"},\\n    \\"method\\": \\"POST\\",\\n    \\"principalId\\": \\"\\",\\n    \\"stage\\": \\"local\\",\\n\\n    \\"cognitoPoolClaims\\" : {\\n\\n       \\"sub\\": \\"\\"\\n    },\\n\\n        \\"enhancedAuthContext\\":     {\\n        }\\n  ,\\n\\n        \\"headers\\":     {\\n        }\\n  ,\\n\\n        \\"query\\":     {\\n        }\\n  ,\\n\\n        \\"path\\":     {\\n    \\n                        \\"\\"proxy\\"\\":\\n          \\"\\"test\\"\\"\\n                  }\\n  ,\\n\\n        \\"identity\\":     {\\n    \\n                        \\"\\"accountId\\"\\":\\n          \\"0\\"\\n           ,     \\n                        \\"\\"sourceIp\\"\\":\\n          \\"\\"172.17.0.1\\"\\"\\n           ,     \\n                        \\"\\"userAgent\\"\\":\\n          \\"\\"curl/7.84.0\\"\\"\\n                  }\\n  ,\\n\\n        \\"stageVariables\\":     {\\n        }\\n  ,\\n\\n    \\"requestPath\\": \\"/{proxy+}\\"\\n  }\\n", "__type": "InvalidRequest"}', headers={'Content-Type': 'text/html; charset=utf-8', 'x-amzn-errortype': 'InvalidRequest', 'Content-Length': '1108', 'Connection': 'close'})
```

### Expected Behavior

The template should render a proper JSON document

### How are you starting LocalStack?

Custom (please describe below)

### Steps To Reproduce

#### How are you starting localstack (e.g., `bin/localstack` command, arguments, or `docker-compose.yml`)

    LS_LOG=trace-internal localstack start

#### Client commands (e.g., AWS SDK code snippet, or sequence of "awslocal" commands)

    - localstack-terraform-samples/apigateway-lambda-velocity $ terraform init; terraform plan; terraform apply --auto-approve
   - localstack-terraform-samples/apigateway-lambda-velocity $ curl -X POST "9b2k2o2wd1.execute-api.localhost.localstack.cloud:4566/local/test" -H 'content-type: application/json' -d '{ "greeter": "cesar" }'

*** APIGW ID is taked from the terraform apply output


### Environment

```markdown
- OS: Macos 13.0.1
- LocalStack: 1.2.1.dev 
- Docker Desktop: v4.13.1
```


### Anything else?

Searching for velocity bug, I encountered bug https://github.com/localstack/localstack/issues/5587 which is resolved but actually the bug is still there.
pass
    def __init__(self, passthrough_behaviour: str):
        self.passthrough_behavior = self.get_passthrough_behavior(passthrough_behaviour)
    def check_passthrough_behavior(self, request_template):
        """
        Specifies how the method request body of an unmapped content type will be passed through
        the integration request to the back end without transformation.
        A content type is unmapped if no mapping template is defined in the integration or the
        content type does not match any of the mapped content types, as specified in requestTemplates
        """
        if not request_template and self.passthrough_behavior in {
            PassthroughBehavior.NEVER,
            PassthroughBehavior.WHEN_NO_TEMPLATES,
        }:
            raise MappingTemplates.UnsupportedMediaType()
    @staticmethod
    def get_passthrough_behavior(passthrough_behaviour: str):
        return getattr(PassthroughBehavior, passthrough_behaviour, None)
class VelocityUtilApiGateway(VelocityUtil):
    """
    Simple class to mimic the behavior of variable '$util' in AWS API Gateway integration
    velocity templates.
    See: http://docs.aws.amazon.com/apigateway/latest/developerguide/api-gateway-mapping-template-reference.html
    """
    def base64Encode(self, s):