docs: improve Codex integration with MCP-first guidance

[nvandessel]

Summary

• update Codex integration docs from static-only language to MCP-capable + no lifecycle hooks
• add dedicated Codex guide: docs/integrations/codex.md
• add Codex orchestration templates:
  • docs/integrations/templates/codex-agents.md.template
  • docs/integrations/templates/floop.SKILL.md.template
• align core docs with the new model:
  • docs/integrations/README.md
  • docs/integrations/agent-prompt-template.md
  • AGENTS.md
• add Codex quick-install UX (copy/paste setup, restart, verify, update, uninstall)

Why

Codex can call MCP tools, but lacks Claude-style hook events. This change documents and templates the pseudo-hook cadence (floop_active at task/context boundaries, floop_learn on correction, floop_feedback after behavior outcomes) so teams can run floop reliably in Codex.

Validation

• verified in a live Codex session that MCP can read global-store frond behaviors via floop_list(tag="frond")
• docs/template consistency pass completed
• docs/templates-only PR (no runtime code changes)

[greptile-apps]

Greptile Summary

This PR updates Codex integration documentation to reflect MCP support with instruction-based orchestration. The changes establish a dual-layer approach for Codex: MCP tools for bidirectional floop access, and explicit runtime cadence rules to compensate for the absence of lifecycle hooks.

Key additions:

• New comprehensive codex.md guide with MCP setup, verification steps, and dogfooding workflow
• Codex-specific AGENTS template defining pseudo-hook cadence for task start, context changes, corrections, and feedback
• Codex skill template (floop.SKILL.md.template) for stronger workflow enforcement
• Updated compatibility matrix showing Codex as MCP-capable
• CLI fallback documentation throughout for hookless environments

All changes are documentation and templates only, with no code modifications. References to floop MCP tools (floop_active, floop_learn, floop_feedback, floop_validate, etc.) are accurate and match the existing schema.

Confidence Score: 5/5

• This PR is safe to merge with no risk
• Documentation-only changes with no code modifications. All technical references (MCP tools, file paths, configuration formats) are accurate and consistent. The documentation is well-structured, comprehensive, and follows existing patterns in the repository.
• No files require special attention

Important Files Changed

Filename	Overview
AGENTS.md	Updated integration language to reflect MCP+hooks approach and added Codex runtime cadence section with pseudo-hook workflow
docs/integrations/README.md	Updated Codex compatibility matrix entry to show MCP support and updated description with link to new codex.md guide
docs/integrations/agent-prompt-template.md	Removed Codex from non-MCP tools list, fixed agents.md capitalization, and added Codex Note section with MCP guidance
docs/integrations/codex.md	New comprehensive integration guide covering MCP setup, verification, orchestration rules, optional skill installation, CLI fallback, and dogfooding workflow
docs/integrations/templates/codex-agents.md.template	New template for Codex-specific AGENTS.md content defining required cadence for task start, context shifts, corrections, and behavior outcomes
docs/integrations/templates/floop.SKILL.md.template	New Codex skill template enforcing floop operational loop for hookless environments with bootstrap, refresh, capture, and feedback stages

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[greptile-apps]

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