Fix Gevent patch regression with correct import order

[srprash]

Issue

This PR first fixed the Gevent monkey patching issue by calling the patch operation when the ADOT Python starts up and before the modules are loaded.
Later on in v0.10.0, this commit broke the above fix by adding
the line from amazon.opentelemetry.distro.aws_opentelemetry_configurator which transitively imports the requests library before the gevent patch operation is called, causing inconsistencies in the patched libraries resulting in seeing the RecursionError: maximum recursion depth exceeded error reappearing.

Changes

1. Adding back the earlier logic to run the gevent's monkey patch (only if gevent is installed) which was removed in this commit to unblock development.
2. Refactoring the patch into its own file and adding comprehensive comments to avoid the same issue in future.
3. Updated unit tests to mock the gevent module and validate only the ADOT logic without running the gevent monkey patch. The actual behavior of the patch should be tested in a higher level test such as a contract test.

Testing

Did a manual E2E testing using a sample flask application. Confirmed the following:

• Saw RecursionError in the application with ADOT Python v0.10.0
• No such error when using ADOT with this fix.

Setup

Sample app

from flask import Flask, request, jsonify
import logging
import sys
from datetime import datetime

import requests

# Configure logging
logging.basicConfig(
    level=logging.INFO,
    format='%(asctime)s - %(name)s - %(levelname)s - %(message)s'
)

app = Flask(__name__)
logger = logging.getLogger(__name__)

@app.route('/requests')
def make_request():
    res = requests.get('https://httpbin.org/get', timeout=5)
    return jsonify({
        'status': 'success',
        'status_code': res.status_code,
        'url': res.url,
        'timestamp': datetime.now().isoformat()
    })

if __name__ == '__main__':
    app.run(debug=False, host='0.0.0.0', port=5001)

Running with problematic version (see the MonkeyPatchWarning)

((venv) ) ➜  flask git:(fix_gevent_regression) ✗ opentelemetry-instrument gunicorn -w 1 -k gevent --bind 0.0.0.0:5001 app:app
/Users/srprash/aws-otel-python-instrumentation/venv/lib/python3.12/site-packages/amazon/opentelemetry/distro/patches/_instrumentation_patch.py:36: MonkeyPatchWarning: Monkey-patching ssl after ssl has already been imported may lead to errors, including RecursionError on Python 3.6. It may also silently lead to incorrect behaviour on Python 3.7. Please monkey-patch earlier. See https://github.com/gevent/gevent/issues/1016. Modules that had direct imports (NOT patched): ['urllib3.util.ssl_ (/Users/srprash/aws-otel-python-instrumentation/venv/lib/python3.12/site-packages/urllib3/util/ssl_.py)', 'urllib3.util (/Users/srprash/aws-otel-python-instrumentation/venv/lib/python3.12/site-packages/urllib3/util/__init__.py)']. 
  monkey.patch_all()
Failed to get k8s token: [Errno 2] No such file or directory: '/var/run/secrets/kubernetes.io/serviceaccount/token'
AwsEksResourceDetector failed: [Errno 2] No such file or directory: '/var/run/secrets/kubernetes.io/serviceaccount/token'
AwsEcsResourceDetector failed: Missing ECS_CONTAINER_METADATA_URI therefore process is not on ECS.
AwsEc2ResourceDetector failed: <urlopen error [Errno 65] No route to host>
[2025-10-29 11:00:55 -0700] [54080] [INFO] Starting gunicorn 23.0.0
[2025-10-29 11:00:55 -0700] [54080] [INFO] Listening at: http://0.0.0.0:5001 (54080)
[2025-10-29 11:00:55 -0700] [54080] [INFO] Using worker: gevent
[2025-10-29 11:00:55 -0700] [54290] [INFO] Booting worker with pid: 54290
2025-10-29 11:02:12,464 - app - ERROR - Exception on /requests [GET]

Running with the fix

((venv) ) ➜  flask git:(fix_gevent_regression) ✗ opentelemetry-instrument gunicorn -w 1 -k gevent --bind 0.0.0.0:5001 app:app
Failed to get k8s token: [Errno 2] No such file or directory: '/var/run/secrets/kubernetes.io/serviceaccount/token'
AwsEksResourceDetector failed: [Errno 2] No such file or directory: '/var/run/secrets/kubernetes.io/serviceaccount/token'
AwsEcsResourceDetector failed: Missing ECS_CONTAINER_METADATA_URI therefore process is not on ECS.
AwsEc2ResourceDetector failed: <urlopen error [Errno 65] No route to host>
[2025-10-29 11:04:45 -0700] [60707] [INFO] Starting gunicorn 23.0.0
[2025-10-29 11:04:45 -0700] [60707] [INFO] Listening at: http://0.0.0.0:5001 (60707)
[2025-10-29 11:04:45 -0700] [60707] [INFO] Using worker: gevent
[2025-10-29 11:04:45 -0700] [60734] [INFO] Booting worker with pid: 60734

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