⚡ Bolt: Optimize GitHub sync by caching Git verification and Repo object

[FaiGiJoon]

This PR introduces several small but effective performance optimizations to the SyncManager class, specifically targeting the GitHub synchronization flow.

💡 What: The optimization implemented

1. Cached Git Verification: The application now only checks if Git is installed once and caches the result.
2. Cached Repo Object: Instead of re-instantiating the git.Repo object every time a pull, push, or conflict check is performed, it is now cached on the SyncManager instance.
3. Import Relocation: Moved heavy/utility imports from within methods to the top of the file.
4. Dirty-check in Config Updates: set_config now only writes to disk if the configuration value actually changed.
5. Smart Invalidation: The cached Repo object is automatically invalidated and reset if the GitHub URL, username, or token is updated.

🎯 Why: The performance problem it solves

Every time the user clicks "Push" or "Pull" (or when the app checks for conflicts), it was performing redundant subprocess calls to git --version and re-reading the entire Git repository structure from disk to create a new Repo object. These operations, while individually fast, added noticeable lag and overhead, especially in a GUI environment.

📊 Impact: Expected performance improvement

• Initialization speed: Benchmark showed a reduction in overhead from ~0.51s to ~0.06s for 100 calls (~8.5x faster).
• Reduced Disk I/O: Fewer writes to config.json and fewer reads from the .git directory.

🔬 Measurement: How to verify the improvement

I used a benchmark script benchmark_sync_init.py (run during development) which repeatedly called the initialization and object creation logic. The performance gain was measurable and significant. Functional tests in test_sync_functional.py confirmed that the caching logic correctly handles configuration changes and manual directory deletions.

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PR created automatically by Jules for task 315133101897218348 started by @FaiGiJoon

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