docs(claude): register The Booth under Global tools available

Add a fleet-tool entry for The Booth (nh3-dev :8090 ephemeral media board) so
any Claude Code session can surface A/B renders, smoke results, and audio/video
to the operator by dropping a folder in ~/booth-data.

home_root/.claude/CLAUDE.md

@@ -395,6 +395,22 @@ note says otherwise. On other boxes, check first.)
   this before spending premium API tokens on tasks a small fast local model
   handles fine (the LLM-last-resort floor still applies — deterministic first).
 
+- **The Booth** — ephemeral media board for surfacing **A/B renders, smoke
+  results, screenshots, audio/video** to the operator (live at
+  `http://10.100.10.50:8090/`, Homepage → *Apps → The Booth*). A booth is
+  *just a folder* — no upload API: any session drops files into
+  `~/booth-data/<name>/` on **nh3-dev** (or from another host
+  `rsync -a ./out/ nh3-dev:booth-data/<name>/`), then hands the operator
+  `http://10.100.10.50:8090/b/<name>/`. A folder's own `index.html` is served
+  verbatim (build a custom report); otherwise it auto-renders a gallery of
+  images / webm+mp4 video / audio, with a `<file>.txt` sidecar folded in as
+  that item's caption (labels A/B pairs). Wiped **24h after last activity**.
+  No auth — LAN/WG-internal + ephemeral, so don't drop secrets in a booth.
+  Reach for it instead of describing results in prose when a picture, clip, or
+  side-by-side would land faster. Code + helper CLI: eshpfi
+  `services/booth/` (`scripts/booth {new|add|url|ls|rm}`); user-level systemd
+  on nh3-dev (`systemctl --user status booth.service`).
+
 ## DevOps delegation
 
 For all DevOps work — deployments, infrastructure provisioning,