fix(deploy): sync static assets and nginx CSS route

Copy .next/static and public into standalone after build; serve
/_next/static from nginx; verify CSS in install.sh.

Co-authored-by: Cursor <cursoragent@cursor.com>

scripts/sync-standalone-assets.sh

@@ -0,0 +1,29 @@
+#!/usr/bin/env bash
+# Copy Next.js static assets into standalone output (required for `node server.js`).
+set -euo pipefail
+
+ROOT="${1:-$(cd "$(dirname "$0")/.." && pwd)}"
+STANDALONE="${ROOT}/.next/standalone"
+STATIC_SRC="${ROOT}/.next/static"
+PUBLIC_SRC="${ROOT}/public"
+
+if [[ ! -d "${STANDALONE}" ]]; then
+  echo "[sync-standalone-assets] No .next/standalone — skipping (non-standalone build?)" >&2
+  exit 0
+fi
+
+if [[ ! -d "${STATIC_SRC}" ]]; then
+  echo "[sync-standalone-assets] ERROR: missing ${STATIC_SRC} — run npm run build first" >&2
+  exit 1
+fi
+
+mkdir -p "${STANDALONE}/.next"
+rm -rf "${STANDALONE}/.next/static"
+cp -a "${STATIC_SRC}" "${STANDALONE}/.next/static"
+
+if [[ -d "${PUBLIC_SRC}" ]]; then
+  rm -rf "${STANDALONE}/public"
+  cp -a "${PUBLIC_SRC}" "${STANDALONE}/public"
+fi
+
+echo "[sync-standalone-assets] OK: .next/static + public → ${STANDALONE}"