fix(mcp): support partial readiness and align embedder Info cache with real state

[esifea]

Summary

• What changed:
  • Boot injects each adapter as it becomes ready
  • Embedder Info cache stores only success
• Why:
  • /rune:diagnostics cannot check partial readiness with all-or-nothing approach
  • Info cache is never updated with sync.Once
• Scope:

Validation

• Tests run (or explain why not):
• Docs updated (if behavior/setup changed)

Cross-Agent Invariants

• scripts/bootstrap-mcp.sh remains the single source of truth for runtime prep (venv/deps/self-heal)
• No agent-specific script duplicates bootstrap/setup logic
• Agent-specific scripts remain thin adapters (registration/wiring only)
• Codex-only commands (codex mcp ...) are clearly separated from cross-agent/common instructions
• Claude/Gemini/OpenAI instructions do not include Codex-only commands
• SKILL.md, commands/rune/*.toml, and AGENT_INTEGRATION.md stay consistent on boundaries

Notes for Reviewers

• Risk areas:
• Backward compatibility impact:
• Follow-up work (if any): staleClientCloseTime is changed to 30s to avoid race, but it should be reverted once closeAfterInterval is implemented with refcount/WaitGroup