P1-T4: Update docs to reflect broker robustness improvements

[SoundBlaster]

Description

Update 5 docs/ files and 4 DocC mirror files to reflect the Phase 2 broker robustness improvements shipped in P2-T1 through P2-T5:

• --broker flag (P2-T1) added to mode tables, client examples, migration guides, and topology sections. --broker-connect/--broker-spawn demoted to legacy aliases.
• Stale socket auto-recovery (P2-T2) — limitations and troubleshooting sections updated; manual cleanup noted as only needed for --broker-connect.
• JSON-RPC -32001 error (P2-T4) — "Could not connect" troubleshooting entries updated to show the actual error response format.
• Web-UI mismatch warning (P2-T5) — new troubleshooting entry added: "Warning: broker is running without --web-ui on port N".

Files changed: docs/broker-mode.md, docs/troubleshooting.md, docs/cursor-setup.md, docs/claude-setup.md, docs/codex-setup.md, and their four DocC mirrors.

Follow-up tasks P1-T5 (Medium) and P1-T6 (Low) added to workplan for two remaining minor gaps found during review.

Type of Change

• Bug fix
• New feature
• Documentation update
• Refactoring
• CI/CD improvement

Quality Gates

• make test - 737 passed, 5 skipped, 91.3% coverage (≥90% required)
• make lint - ruff check src/ clean
• make format - N/A (no source changes)
• make typecheck - N/A (no source changes)
• make doccheck - make doccheck-all passed across all scopes

Documentation Sync

• Documentation changes are synced with DocC catalog

docs/ file	DocC file	Synced
docs/cursor-setup.md	CursorSetup.md	✅
docs/claude-setup.md	ClaudeCodeSetup.md	✅
docs/codex-setup.md	CodexCLISetup.md	✅
docs/troubleshooting.md	Troubleshooting.md	✅

Testing

• Added/updated tests for new functionality — N/A (docs only)
• All tests pass locally — 737 passed, 5 skipped
• Manually tested the changes — N/A (docs only)

Checklist

• Code follows the project's style guidelines
• Self-review completed
• Comments added for complex code — N/A
• Documentation updated (if needed)
• No new warnings generated
• PR title is descriptive

[chatgpt-codex-connector]

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