### 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.
import base64
import datetime
import json
import logging
import re
import time
from enum import Enum
from typing import Any, Dict, Optional, Tuple, Union
import pytz
import requests
from flask import Response as FlaskResponse
from moto.apigateway.models import apigateway_backends
from requests.models import Response
from six.moves.urllib_parse import urljoin
from localstack import config
from localstack.constants import (
    APPLICATION_JSON,
    HEADER_LOCALSTACK_EDGE_URL,
    LOCALHOST_HOSTNAME,
    PATH_USER_REQUEST,