### Is there an existing issue for this?

- [X] I have searched the existing issues

### Current Behavior

I am trying to build an API Gateway HTTP Proxy fallback for a REST API. I have the following API Gateway resources configured locally with localstack.

```json
{
  "httpMethod": "ANY",
  "authorizationType": "NONE",
  "apiKeyRequired": false,
  "requestParameters": {
    "method.request.path.proxy": true
  },
  "methodIntegration": {
    "type": "HTTP_PROXY",
    "httpMethod": "ANY",
    "uri": "https://httpbin.org/anything/{proxy}",
    "requestParameters": {
      "integration.request.path.proxy": "method.request.path.proxy"
    },
    "passthroughBehavior": "WHEN_NO_MATCH",
    "timeoutInMillis": 29000,
    "cacheNamespace": "9b6e854f",
    "cacheKeyParameters": []
  }
}

```

When I call this endpoint with `GET http://localhost:4566/restapis/vt7zvfoavm/local/_user_request_/foo/bar/baz?myParam=12345678` I receive the following response (Using [HTTPbin](https://httpbin.org/) here to return the request as the response)

```jsonc
{
    "args": {}, // no query params in args
    "data": "",
    "files": {},
    "form": {},
    "headers": {
        "--Apigw-Request-Region--": "eu-west-1",
        "Accept": "*/*",
        "Accept-Encoding": "gzip, deflate, br",
        "Authorization": "AWS4-HMAC-SHA256 Credential=__internal_call__/20160623/us-east-1/apigateway/aws4_request, SignedHeaders=content-type;host;x-amz-date;x-amz-target, Signature=1234",
        "Host": "localhost",
        "Postman-Token": "134b9852-7589-4a54-b730-5444588ae024",
        "Remote-Addr": "172.17.0.1",
        "User-Agent": "PostmanRuntime/7.28.4",
        "X-Amzn-Trace-Id": "Root=1-61b9bc31-6c2834ad38c63f456284cdd9",
        "X-Localstack-Edge": "http://localhost:4566",
        "X-Localstack-Tgt-Api": "apigateway"
    },
    "json": null,
    "method": "GET",
    "origin": "172.17.0.1, localhost:4566, 127.0.0.1, localhost:4566, 92.27.80.225",
    "url": "https://localhost/anything/foo/bar/baz" // no query params on url
}
```

The query parameter `myParam=12345678` is stripped from the request, despite being a valid part of the `{proxy}` path.

I used the same configuration to create resources in AWS:

```json
{
  "httpMethod": "ANY",
  "authorizationType": "NONE",
  "apiKeyRequired": false,
  "requestParameters": {
    "method.request.path.proxy": true
  },
  "methodIntegration": {
    "type": "HTTP_PROXY",
    "httpMethod": "ANY",
    "uri": "https://httpbin.org/anything/{proxy}",
    "connectionType": "INTERNET",
    "requestParameters": {
      "integration.request.path.proxy": "method.request.path.proxy"
    },
    "passthroughBehavior": "WHEN_NO_MATCH",
    "timeoutInMillis": 29000,
    "cacheNamespace": "445f0a",
    "cacheKeyParameters": []
  }
}
```

And the response is as expected:

```jsonc
// GET https://redacted.execute-api.eu-west-1.amazonaws.com/v1/foo/bar/baz?myParam=12345678
{
    "args": {
        "myParam": "12345678" // query param passed through
    },
    "data": "",
    "files": {},
    "form": {},
    "headers": {
        "Accept": "*/*",
        "Accept-Encoding": "gzip, deflate, br",
        "Cloudfront-Forwarded-Proto": "https",
        "Cloudfront-Is-Desktop-Viewer": "true",
        "Cloudfront-Is-Mobile-Viewer": "false",
        "Cloudfront-Is-Smarttv-Viewer": "false",
        "Cloudfront-Is-Tablet-Viewer": "false",
        "Cloudfront-Viewer-Country": "GB",
        "Host": "httpbin.org",
        "Postman-Token": "41397d0f-d04b-4b39-8110-5a5d9684e86d",
        "User-Agent": "PostmanRuntime/7.28.4",
        "X-Amz-Cf-Id": "Sb6KMrHBuK0V1zyn9TdmKm0HreYhZrOmgHHec0mPD5jR0YjGpzDDEg==",
        "X-Amzn-Apigateway-Api-Id": "redacted",
        "X-Amzn-Trace-Id": "Self=1-61b9be60-5a0d8f4d09b8f5c554bbe723;Root=1-61b9be5f-37e6655166d36d2a4b330d4f"
    },
    "json": null,
    "method": "GET",
    "origin": "92.27.80.225, 130.176.222.55, 108.128.160.192",
    "url": "https://httpbin.org/anything/foo/bar/baz?myParam=12345678" // query param on url
}
```

I have also tried explicitly mapping query parameters with `"integration.request.querystring.myParam": "method.request.querystring.myParam"`, this doesn't work and also doubles up the query param in the AWS environment.

### Expected Behavior

I expect query parameters to be passed through on HTTP_PROXY requests as they are in the AWS equivalent.

### 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`)

I'm using `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" "test-api-proxy-resource" {
  rest_api_id = aws_api_gateway_rest_api.test-api.id
  parent_id   = aws_api_gateway_rest_api.test-api.root_resource_id
  path_part   = "{proxy+}"
}

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

  request_parameters = {
    "method.request.path.proxy" = true
  }
}

resource "aws_api_gateway_integration" "test-api-proxy-method-integration" {
  rest_api_id             = aws_api_gateway_rest_api.test-api.id
  resource_id             = aws_api_gateway_resource.test-api-proxy-resource.id
  http_method             = aws_api_gateway_method.test-api-proxy-method.http_method
  type                    = "HTTP_PROXY"
  integration_http_method = "ANY"
  uri                     = "https://httpbin.org/anything/{proxy}"
  passthrough_behavior    = "WHEN_NO_MATCH"
  request_parameters = {
    "integration.request.path.proxy" = "method.request.path.proxy"
  }
}
```

I use `aws{local} apigateway get-method --rest-api-id <ID> --resource-id <ID> --http-method ANY` to get the configuration out of the environment.


### Environment

```markdown
- OS: macOS 12.0.1
- LocalStack: 0.13.1 and 0.13.0.11
```


### Anything else?

_No response_
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,