### Is there an existing issue for this?

- [X] I have searched the existing issues

### Current Behavior

I'm trying to use the HTTP_PROXY feature to provide a fallback to an old API whilst the endpoints are replaced with API GW + Lambda.

I currently have an API Gateway set up similar to the following:

```
/resource
    /{proxy+}
        ANY -> HTTP_PROXY
    /test
        GET -> AWS_PROXY -> Lambda
```

When I do a request to `http://localhost:4566/restapis/uslhbxmpgd/v1/_user_request_/resource/test` the `{proxy+}` resource catches the request.

I have tested the configuration in AWS and this behaviour isn't present. The `/test` catches the request and forwards an event through to the Lambda Integration.

### Expected Behavior

`{proxy+}` to have lowest possible specificity if other resources are defined at the same level, meaning it should only catch requests that don't have another matching resource.

### How are you starting LocalStack?

With the `localstack` script

### Steps To Reproduce

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

    localstack start

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

I'm using terraform to configure the environments:

```hcl
resource "aws_api_gateway_resource" "resource" {
  rest_api_id = aws_api_gateway_rest_api.api.id
  parent_id   = aws_api_gateway_rest_api.api.root_resource_id
  path_part   = "resource"
}

resource "aws_api_gateway_resource" "fallback-proxy-resource" {
  rest_api_id = aws_api_gateway_rest_api.api.id
  parent_id   = aws_api_gateway_resource.resource.id
  path_part   = "{proxy+}"
}

resource "aws_api_gateway_method" "fallback-proxy-method" {
  rest_api_id   = aws_api_gateway_rest_api.api.id
  resource_id   = aws_api_gateway_resource.fallback-proxy-resource.id
  http_method   = "ANY"
  authorization = "NONE"

  request_parameters = {
    "method.request.path.proxy"           = true
    "method.request.header.authorization" = false
  }
}

resource "aws_api_gateway_integration" "fallback-proxy-method-integration" {
  rest_api_id             = aws_api_gateway_rest_api.api.id
  resource_id             = aws_api_gateway_resource.fallback-proxy-resource.id
  http_method             = aws_api_gateway_method.fallback-proxy-method.http_method
  type                    = "HTTP_PROXY"
  integration_http_method = "ANY"
  uri                     = "https://httpbin.org/anything/{proxy}"

  request_parameters = {
    "integration.request.path.proxy"           = "method.request.path.proxy"
    "integration.request.header.authorization" = "method.request.header.authorization"
  }
}

resource "aws_api_gateway_resource" "test-resource" {
  rest_api_id = aws_api_gateway_rest_api.api.id
  parent_id   = aws_api_gateway_resource.resource.id
  path_part   = "test"
}

resource "aws_api_gateway_method" "test-GET-method" {
  rest_api_id   = aws_api_gateway_rest_api.api.id
  resource_id   = aws_api_gateway_resource.test-resource.id
  http_method   = "GET"
  authorization = "NONE"
}

resource "aws_api_gateway_integration" "test-GET-method-integration" {
  rest_api_id             = aws_api_gateway_rest_api.api.id
  resource_id             = aws_api_gateway_resource.test-resource.id
  http_method             = aws_api_gateway_method.test-GET-method.http_method
  integration_http_method = "POST"
  type                    = "AWS_PROXY"
  uri                     = "arn..."
}
```


### Environment

```markdown
- OS: macOS 12.0.1
- LocalStack: 0.13.3 and 0.13.2
```


### Anything else?

I've tested using versions pre and post the fix for other HTTP proxy issues by @calvernaz in #5212 and it doesn't seem to be related.
if isinstance(self.auth_info, dict):
            if self.auth_info.get("identity") is None:
                self.auth_info["identity"] = {}
            return self.auth_info["identity"]
    def is_websocket_request(self):
        upgrade_header = str(self.headers.get("upgrade") or "")
        return upgrade_header.lower() == "websocket"
    def is_v1(self):
        """Whether this is an API Gateway v1 request"""
        return self.apigw_version == ApiGatewayVersion.V1
class ProxyListenerApiGateway(ProxyListener):
    def forward_request(self, method, path, data, headers):
        invocation_context = ApiInvocationContext(method, path, data, headers)
        forwarded_for = headers.get(HEADER_LOCALSTACK_EDGE_URL, "")
        if re.match(PATH_REGEX_USER_REQUEST, path) or "execute-api" in forwarded_for:
            result = invoke_rest_api_from_request(invocation_context)
            if result is not None:
                return result
        data = data and json.loads(to_str(data))
        if re.match(PATH_REGEX_AUTHORIZERS, path):
            return handle_authorizers(method, path, data, headers)
        if re.match(PATH_REGEX_DOC_PARTS, path):
            return handle_documentation_parts(method, path, data, headers)
        if re.match(PATH_REGEX_VALIDATORS, path):
            return handle_validators(method, path, data, headers)
        if re.match(PATH_REGEX_RESPONSES, path):
            return handle_gateway_responses(method, path, data, headers)
        if re.match(PATH_REGEX_PATH_MAPPINGS, path):