[CI] Handle failure to download Playwright dependencies

[Copilot]

This PR implements caching for Playwright dependencies in GitHub Actions workflows to prevent repeated downloads and handle network failures gracefully.

Changes

1. Added Caching Mechanism

   • Created a reusable workflow (setup-playwright-cache.yml) that caches Playwright dependencies per OS
   • Added daily scheduled workflow (cache-playwright-deps.yml) to refresh the cache
   • Modified run-tests.yml to use cached dependencies

2. Improved Reliability

   • Added retry mechanism with exponential backoff for dependency downloads
   • Enabled enhanced NuGet retry settings to handle transient network issues
   • Set cache keys based on OS and date for proper invalidation

3. Configuration

   • Cache refreshes daily to ensure dependencies stay updated
   • Added manual workflow trigger to force cache refresh when needed
   • Implemented OS-specific caching for Windows, macOS, and Ubuntu

This should prevent test failures due to timeouts when downloading Playwright dependencies by only downloading once per day per OS and using cached versions for all test runs.

Fixes #9257.

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