feat(gateway-chat): persistent static-serve stack for the model-smoking web chat

Stands up tools/gateway-chat.html as a permanent URL on ana-docker (http://10.250.50.70:8091)
via a tiny nginx:alpine static container (no GPU, no DB). conf/index.html is a deployed
mirror of tools/gateway-chat.html (re-sync one-liner in README). Homepage tile + tnet per
convention. The enhanced tool (auto-discovers /v1/models, system prompts, streaming +
reasoning, image upload for vision) is now always-on for smoking new gateway models.

stacks/gateway-chat/README.md

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+# gateway-chat
+
+Persistent static-serve of **`tools/gateway-chat.html`** — the zero-dependency web chat
+for **smoking models on the LiteLLM gateway** (`10.250.50.70:4000`). It auto-discovers
+every gateway model via `/v1/models` (the ↻ control — new models just appear), takes
+system prompts, streams responses (renders `reasoning_content`), and supports image
+upload for vision models (Qwopus, image-judge). It deliberately never sends a `tools`
+field, sidestepping the vLLM empty-`tools` 400.
+
+- **Host:** ana-docker (non-GPU)
+- **URL:** http://10.250.50.70:8091
+- **Image:** `nginx:alpine` (tiny static server — no GPU, no DB)
+- **Served file:** `conf/index.html` → mounted read-only at
+  `/usr/share/nginx/html/index.html`
+
+## The served file mirrors `tools/gateway-chat.html`
+
+The canonical/editable source is the repo's **`tools/gateway-chat.html`** (also openable
+`file://` or via `python3 -m http.server -d tools`). `conf/index.html` here is the
+deployed copy. After editing the tool, re-sync + redeploy:
+
+```bash
+cp tools/gateway-chat.html stacks/gateway-chat/conf/index.html
+scripts/deploy-stack.sh ana-docker gateway-chat --conf
+```
+
+No restart needed — the file is bind-mounted, so nginx serves the new content on the next
+request. (Restart only if you want a forced reload.)
+
+## Deploy
+
+```bash
+scripts/deploy-stack.sh ana-docker gateway-chat            # compose + conf
+ssh ana-docker 'cd /opt/docker/compose/gateway-chat && docker compose up -d'
+```
+
+Set the gateway base URL + an API key in the page's sidebar (persists in `localStorage`),
+then hit ↻ to load the model list.