[DX] Add `apc doctor` command for environment diagnostics

[FZ2000]

Problem

There's no way for a user to verify their APC installation is healthy. Common failure scenarios:

• Python version is too old (requires 3.12+, but error only surfaces when running commands)
• OS keychain is unavailable (Linux without libsecret, WSL, headless CI)
• age binary missing (needed for export/import encryption)
• No LLM configured (silent failure: apc memory sync quietly does nothing)
• ~/.apc/ directory corrupted / permissions issue

Currently a new user has to discover these issues one by one, command by command.

Suggested Fix

Add apc doctor that prints a system health report:

$ apc doctor

  System Checks
  ─────────────
  ✓ Python 3.12.2 (required: 3.12+)
  ✓ apc cache directory: ~/.apc/ (exists, writable)
  ✓ OS keychain: available (macOS Keychain)
  ✗ age binary: not found — export/import encryption unavailable
    → Install: brew install age
  ✓ LLM configured: anthropic/claude-sonnet-4-6
  
  Detected Tools
  ──────────────
  ✓ claude-code: ~/.claude/
  ✓ cursor: ~/.cursor/
  ✗ gemini-cli: not installed

This is a common pattern in developer CLIs (e.g., brew doctor, flutter doctor, rails doctor) and dramatically improves first-run success rate.