chore: extract the Booth to its own repo (vh/booth)

The Booth is now one of the most-used fleet tools -- 17 agent handles post to
it daily -- and it is taking an information-architecture rework plus a
cross-agent SVOS design retrofit from design-dev. That work wants its own
ROADMAP, contracts and blast radius, not the fleet-infrastructure repo's.

All 29 commits moved with it via `git subtree split`; the history carries real
lessons (two shipped-dead controls, the verbatim-injection traps) that a
squashed import would have thrown away.

Live service repointed and verified: the user unit and the ~/.local/bin/booth
symlink now resolve into ~/development/booth, healthz answers, all 24 booths
intact. services/booth/ keeps a pointer README, same shape as the
chatterbox-fast and tts-stack extractions.

servers/nh3-dev/README.md

@@ -136,13 +136,13 @@ local Bash already executes here — no SSH-to-self needed for non-privileged wo
 - **bloom_music dev** — `~/development/bloom_music`; its `web/` test harness uses
   Playwright headless Chromium for OSMD browser-geometry assertions.
 - **The Booth** — ephemeral media drop board (`:8090`, `booth.service`), from
-  eshpfi `services/booth/`. Lets CC sessions surface A/B renders + smoke results
+  `~/development/booth` (gitea `vh/booth`, extracted from eshpfi 2026-09-21). Lets CC sessions surface A/B renders + smoke results
   (and browser uploads for pickup) to the operator; 24h TTL, Homepage-linked.
   Since 2026-09-09 it also carries **asks** — a session poses a multiple-choice
   question in a booth, the operator answers a radio form + notes in the browser,
   and the pick lands as an answer sidecar the session reads (`booth ask` /
   `booth answer --wait`). ⚠ The **`booth` CLI is on PATH via
-  `~/.local/bin/booth` → `services/booth/scripts/booth`**, symlinked 2026-09-09;
+  `~/.local/bin/booth` → `~/development/booth/scripts/booth`**, symlinked 2026-09-09;
   before that it was on no PATH at all, so every session following the global
   link-board convention was hitting `command not found` unless it used the full
   path. `~/.zshenv` puts `~/.local/bin` in PATH for non-interactive `ssh nh3-dev