### Is there an existing issue for this?

- [X] I have searched the existing issues

### Current Behavior

Deploying a AWS Sam template to localstack via cloudformation results in an API Gateway deploy that does not invoke the function. Subsequently, all requests return an `Unable to find integration for: GET /foo/bar` error. If I specify `GET` for the lambda invocation eventsource method instead of `ANY`, requests go through, but I need to use `GET` and `PUT`.

### Expected Behavior

The specified lambda function should be invoked regardless of the HTTP method used.

### 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`)

    DEBUG=1 localstack start

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

    sam build
    samlocal deploy --resolve-s3 --capabilities CAPABILITY_IAM --stack-name $(PROJECT_NAME) --region us-east-1 -t .aws-sam/build/template.yaml
    


### Environment

```markdown
- OS: Linux (Ubuntu)
- LocalStack: 0.12.20
```


### Anything else?

`awslocal apigateway get-stages --rest-api-id=xxxxxxx`
```
{
    "item": [
        {
            "deploymentId": "ccjq7wewws",
            "stageName": "Stage",
            "description": "",
            "cacheClusterEnabled": false,
            "methodSettings": {},
            "variables": {}
        },
        {
            "deploymentId": "ccjq7wewws",
            "stageName": "test",
            "description": "",
            "cacheClusterEnabled": false,
            "methodSettings": {},
            "variables": {},
            "tags": {}
        }
    ]
}
```

rendered SAM template after sam build
```
AWSTemplateFormatVersion: 2010-09-09
Transform: AWS::Serverless-2016-10-31
Globals:
  Function:
    Runtime: go1.x
    Environment:
      Variables:
        WORKSPACE: test
        ENVIRONMENT: test
        LOG_LEVEL: debug
Resources:
  Api:
    Type: AWS::Serverless::Function
    Properties:
      Handler: endorsements-api
      FunctionName: endorsements-api
      CodeUri: Api
      Timeout: 30
      Events:
        AllEvents:
          Type: Api
          Properties:
            Path: '{proxy+}'
            Method: ANY
            RestApiId:
              Ref: ApiGateway
    Metadata:
      BuildMethod: makefile
  ApiGateway:
    Type: AWS::Serverless::Api
    Name: endorsements-api-gateway
    Properties:
      Name: endorsements-api-gateway
      StageName: test
      MethodSettings:
      - HttpMethod: *
        ResourcePath: /*
Outputs:
  ApiID:
    Value:
      Ref: ApiGateway
  LocalURI:
    Value:
      Fn::Sub: http://localhost:4566/restapis/${ApiGateway}/test/_user_request_/docs/index.html
  Endpoint:
    Value:
      Fn::Sub: https://${ApiGateway}.execute-api.${AWS::Region}.amazonaws.com/Prod/

```

`awslocal apigateway get-integrations --restapi-id=xxxxxx` shows there is an ANY style integration deployed, though it fails for all requests:
```
{
    "items": [
        {
            "id": "3hocyhz56b",
            "path": "{proxy+}",
            "resourceMethods": {
                "X-AMAZON-APIGATEWAY-ANY-METHOD": {
                    "httpMethod": "X-AMAZON-APIGATEWAY-ANY-METHOD",
                    "apiKeyRequired": false,
                    "methodIntegration": {
                        "type": "aws_proxy",
                        "httpMethod": "X-AMAZON-APIGATEWAY-ANY-METHOD",
                        "uri": "arn:aws:apigateway:us-east-1:lambda:path/2015-03-31/functions/arn:aws:lambda:us-east-1:000000000000:function:endorsements-api/invocations",
                        "requestTemplates": {},
                        "cacheNamespace": "84748f6c",
                        "cacheKeyParameters": [],
                        "integrationResponses": {
                            "200": {
                                "statusCode": 200,
                                "responseTemplates": {}
                            }
                        }
                    }
                }
            }
        }
    ]
}
```
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,