### Is there an existing issue for this?

- [X] I have searched the existing issues

### Current Behavior

When creating an API Gateway with an integration of type AWS to S3, the uri to get objects from an S3 bucket is not working, returning:

`{
    "status": 400,
    "body": "{\"Type\": \"User\", \"message\": \"Error invoking integration for API Gateway ID '3en931aay2': API Gateway AWS integration action URI \\\"arn:aws:apigateway:us-east-1:s3:action/GetObject&Bucket=saxpress-drawio=Key={item}\\\", method \\\"GET\\\" not yet implemented\", \"__type\": \"InvalidRequest\"}",
    "headers": {
        "x-amzn-errortype": "InvalidRequest",
        "Content-Type": "text/html; charset=utf-8",
        "Content-Length": "280"
    }
}`

### Expected Behavior

Retrieve S3 object.

### How are you starting LocalStack?

With a docker-compose file

### Steps To Reproduce

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

```
localstack:
    image: localstack/localstack:latest
    hostname: localstack
    environment:
      - AWS_DEFAULT_REGION=us-east-1
      - EDGE_PORT=4566
      - HOSTNAME_EXTERNAL=localstack
      - SERICES=s3,lambda,apigateway,apigatewayv2
      - DEBUG=1
    ports:
      - '4566-4583:4566-4583'
      - '8055:8080'
    volumes:
      - 'saxpress-localstack-data:/tmp/localstack'
      - '/var/run/docker.sock:/var/run/docker.sock'
      - './.localstack:/docker-entrypoint-initaws.d'
```

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

```
awslocal apigateway create-rest-api --region us-east-1 --name ${API_NAME} --endpoint-url=http://localhost:4566

awslocal apigateway create-resource \
  --region ${REGION} \
  --rest-api-id ${API_ID} \
  --parent-id ${PARENT_RESOURCE_ID} \
  --path-part "{proxy+}"

awslocal apigateway put-method \
  --region ${REGION} \
  --resource-id ${RESOURCE_ID} \
  --rest-api-id ${API_ID} \
  --http-method "GET" \
  --authorization-type "NONE" \
  --request-parameters "method.request.path.proxy=true"

awslocal apigateway put-integration \
  --region ${REGION} \
  --resource-id ${RESOURCE_ID} \
  --rest-api-id ${API_ID} \
  --type "AWS" \
  --http-method "GET" \
  --uri "arn:aws:apigateway:${REGION}:s3:action/GetObject&Bucket=${BUCKET_NAME}=Key={item}" \
  --credentials "${ROLE_ARN}" \
  --integration-http-method "GET" \
  --request-parameters "integration.request.path.item=method.request.queryString.proxy,integration.request.path.object=context.requestId"

awslocal apigateway put-method-response \
  --region ${REGION} \
  --resource-id ${RESOURCE_ID} \
  --rest-api-id ${API_ID} \
  --status-code "200" \
  --http-method "GET" \
  --response-parameters "method.response.header.Content-Type=true" \
  --response-models "application/json=Empty"

awslocal apigateway put-integration-response \
  --region ${REGION} \
  --resource-id ${RESOURCE_ID} \
  --rest-api-id ${API_ID} \
  --status-code "200" \
  --http-method "GET" \
  --response-parameters "method.response.header.Content-Type=integration.response.header.Content-Type"
```

Testing the method:
```
root@localstack:/opt/code/localstack# awslocal apigateway test-invoke-method --rest-api-id ${API_ID} --resource-id ${RESOURCE_ID} --http-method GET --path-with-query-string index.html
{
    "status": 400,
    "body": "{\"Type\": \"User\", \"message\": \"Error invoking integration for API Gateway ID '3en931aay2': API Gateway AWS integration action URI \\\"arn:aws:apigateway:us-east-1:s3:action/GetObject&Bucket=saxpress-drawio=Key={item}\\\", method \\\"GET\\\" not yet implemented\", \"__type\": \"InvalidRequest\"}",
    "headers": {
        "x-amzn-errortype": "InvalidRequest",
        "Content-Type": "text/html; charset=utf-8",
        "Content-Length": "280"
    }
}
```

### Environment

```markdown
- OS: macOS Big Sur
- LocalStack: latest
```


### 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
from urllib.parse import urljoin
import pytz
import requests
from flask import Response as FlaskResponse
from jsonschema import ValidationError, validate
from moto.apigateway.models import apigateway_backends
from requests.models import Response
from localstack import config
from localstack.constants import (
    APPLICATION_JSON,
    HEADER_LOCALSTACK_EDGE_URL,
    LOCALHOST_HOSTNAME,
    PATH_USER_REQUEST,
    TEST_AWS_ACCOUNT_ID,
)
from localstack.services.apigateway import helpers
from localstack.services.apigateway.helpers import (
    API_REGIONS,
    PATH_REGEX_AUTHORIZERS,
    PATH_REGEX_CLIENT_CERTS,
    PATH_REGEX_DOC_PARTS,
    PATH_REGEX_PATH_MAPPINGS,