Add CDP endpoint verification with exponential backoff for managed browsers

[SohamKukreti]

Summary

Managed browsers sometimes failed to start due to timing issues where the browser
process was launched but the CDP endpoint wasn't immediately available, causing
connection failures with "CDP endpoint not ready" errors.

Fixes #1445

Solution

• Added _verify_cdp_ready() method in BrowserManager with exponential backoff
• Implements 5 retry attempts with 1.4x exponential backoff.
• Verifies CDP endpoint availability before attempting connection
• Prevents startup failures due to browser initialization timing

List of files changed and why

browser_manager.py

• Add CDP endpoint verification with retry logic and exponential backoff
• Call verification before connecting to CDP in start() method
• Graceful handling of timing issues during browser startup

tests/browser/test_cdp_strategy.py

• Fix cookie persistence test by adding storage state management
• Fix session management test to work with managed browser architecture
• Add comprehensive CDP timing tests covering:
  • Fast startup scenarios
  • Delayed browser startup simulation
  • Exponential backoff behavior validation
  • Concurrent browser connections
  • Stress testing with multiple successive startups
  • Retry count verification

How Has This Been Tested?

To try to reproduce the issue, you can remove the hardcoded waiting time in browser_manager.py to mimic the browser taking time to open.

• Fixed and ran test_cdp_strategy.py, all tests passed.
• Ran identity_based_browsing.py example.
• Ran custom identity based scripts.

Checklist:

• My code follows the style guidelines of this project
• I have performed a self-review of my own code
• I have commented my code, particularly in hard-to-understand areas
• I have made corresponding changes to the documentation
• I have added/updated unit tests that prove my fix is effective or that my feature works
• New and existing unit tests pass locally with my changes

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✨ Finishing touches

🧪 Generate unit tests

• Create PR with unit tests
• Post copyable unit tests in a comment
• Commit unit tests in branch fix/managed-browser-cdp-timing

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[Chikel]

Hey there, any plans on merging this fix?
This is currently blocking managed browser sessions.