docs(omp): add docs/omp-integration.md, matching sibling CLI docs

OMP was the one external CLI mode with no dedicated user-guide doc, unlike
opencode/pi/grok/deepseek which each have one. Covers install, auth (omp
owns its own entirely - no Codeman-side login flow or bypass switch),
what Codeman wires up (OmpConfig), the exact-id pinning mechanism and the
directory-mangling bug behind it, kill-survival via transcript scanning,
terminal behavior, Docker/remote-SSH cases, and known gaps (no idle hook,
mid-turn kill data loss, unverified symlinked-$HOME behavior).

Cross-referenced from README.md's Multi-CLI doc list and docs/docker-cases.md's
credential-seeding summary (which now also documents OMP's sessions/-is-shared
exception to the seed-everything pattern the other CLIs use).

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

README.md

@@ -437,7 +437,7 @@ PTY Output → 16ms Server Batch → DEC 2026 Wrap → SSE → Client rAF → xt
 - **Background daemon & service install** — `codeman web -d` runs the server detached with a pidfile, `~/.codeman/web.log`, and verified startup (it polls the server until it answers, so a port clash never reads as success); `codeman service install` writes a systemd user unit (Linux) or LaunchAgent (macOS) with your shell's PATH baked in, so an nvm or Homebrew `node`, `tmux` and `claude` are actually found. Secrets are never written into unit files
 - **Self-update** — git-clone installs under systemd/launchd update in place from **App Settings → System → Updates**: it detects the latest release, auto-stashes a dirty tree, and streams build progress across the service restart (npm installs report as non-updatable)
 - **Clone a GitHub repo as a case** — paste a repository URL into **Add Case → Clone Repo** and Codeman clones it into `~/codeman-cases/<name>` and registers it as a normal case, ready to run an agent in. It preflights the URL while you type (tells you whether it can be cloned anonymously and offers the repo's real branches and tags for the optional branch/tag field), fills the case name in from the URL, and lets you pick which CLI the Run button should use. Public repositories over `https://`; Codeman never collects or stores credentials
-- **Multi-CLI** — run **Claude Code**, **OpenCode**, **Codex**, **Antigravity**, **Gemini**, **Pi**, **Grok**, or **OMP** per session; env-var prefixes auto-gate (`CLAUDE_CODE_*` vs `OPENCODE_*` vs `CODEX_*` vs `ANTIGRAVITY_*` vs `GEMINI_*`/`GOOGLE_*` vs `PI_*` vs `GROK_*`/`XAI_*` vs `OMP_*`). See [`docs/opencode-integration.md`](docs/opencode-integration.md), [`docs/pi-integration.md`](docs/pi-integration.md) and [`docs/grok-integration.md`](docs/grok-integration.md)
+- **Multi-CLI** — run **Claude Code**, **OpenCode**, **Codex**, **Antigravity**, **Gemini**, **Pi**, **Grok**, or **OMP** per session; env-var prefixes auto-gate (`CLAUDE_CODE_*` vs `OPENCODE_*` vs `CODEX_*` vs `ANTIGRAVITY_*` vs `GEMINI_*`/`GOOGLE_*` vs `PI_*` vs `GROK_*`/`XAI_*` vs `OMP_*`). See [`docs/opencode-integration.md`](docs/opencode-integration.md), [`docs/pi-integration.md`](docs/pi-integration.md), [`docs/grok-integration.md`](docs/grok-integration.md) and [`docs/omp-integration.md`](docs/omp-integration.md)
 - **Docker sessions** — run a case inside an isolated, hardened container. One checkbox on **Create New** spins up a container with sensible defaults and starts the agent inside it; multiple sessions share one per-case container; export a container + its workspace to a portable `.tar.gz` to move it to another machine. See [`docs/docker-cases.md`](docs/docker-cases.md)
 - **Remote SSH sessions** — point a case at another machine and run the agent there inside a durable remote tmux: survives SSH drops, auto-reconnects, and can discover + attach sessions already running on the host. See [`docs/remote-sessions.md`](docs/remote-sessions.md)
 - **Effort & Ultracode** — set a per-session default effort (`low`–`max`) or enable **ultracode** (dynamic multi-agent workflows). Soft defaults only — switchable anytime with `/effort` in-session. Extended-thinking budget is configurable too