docs(deploy): name the retention cron the first mirror fires, and probe the root (FRE-1707)

Two findings from the FRE-1695 review (approved at df788cb6).

1. The mirrored deploy activates a destructive cron the deploy docs never
   mentioned. vercel.json carries two crons: /api/the-nook/lifecycle (13:00
   UTC), already on the tree Vercel builds, and /api/analytics-retention
   (12:00 UTC, 1d9287a / FRE-369), which exists only on Gitea master. The first
   deploy that follows the mirror starts calling it, and the next 12:00 UTC
   deletes every VisitorAnalytics row older than the window —
   ANALYTICS_RETENTION_DAYS, 365 by default — irreversibly and unstaged. The
   behaviour is intended; the silence was not, because the operator is the one
   who presses the button. docs/deploy-source.md "Failure modes" now names the
   cron, the ANALYTICS_RETENTION_SECRET ?? CRON_SECRET bearer check, the 365-day
   default, the fails-closed-without-a-secret path, and that the first run after
   enabling prunes at that default.

2. scripts/verify-deploy.sh could read green with a broken root deploy: it
   probed nook.freno.me, nessa.freno.me/terms and the two remotes, never
   freno.me itself — and FRE-1695's acceptance names the root domain. Adds a
   ROOT_HOST (default https://freno.me) status check ahead of the subdomain
   probes: expects a direct 200, no -L, so a redirect reads as a failure. It
   deliberately does not probe https://freno.me/terms — SITEMAP_ROUTES.main has
   no /terms; Terms of Use is a Nessa surface, so a root /terms 404 is the
   design. The script stays read-only and credential-free.

scripts/verify-deploy.sh

@@ -3,11 +3,13 @@
 #
 # Proves, in one run:
 #   1. Gitea master and GitHub master are the same commit (the mirror converged).
-#   2. The live site serves copy that only exists on the reconciled line:
+#   2. The root domain answers on its own terms: https://freno.me/ returns a direct 200,
+#      so a broken root deploy cannot read as green while the subdomains look fine.
+#   3. The live site serves copy that only exists on the reconciled line:
 #      NOOK-1038's scoped remote claim (GitHub-only before the merge) *and*
 #      FRE-997's "Supported agents" (Gitea-only before the merge). Both at once
 #      can only come from the merge commit.
-#   3. The served tree therefore contains FRE-371 (`2fd2a4a`), which is an
+#   4. The served tree therefore contains FRE-371 (`2fd2a4a`), which is an
 #      ancestor of that merge — checked locally when the commit is in the object
 #      store, so run this from a freno-dev checkout.
 #
@@ -17,6 +19,7 @@ set -uo pipefail
 
 GITEA_REMOTE="${GITEA_REMOTE:-https://git.freno.me/Mike/freno-dev.git}"
 GITHUB_REMOTE="${GITHUB_REMOTE:-https://github.com/mikefreno/freno-dev.git}"
+ROOT_HOST="${ROOT_HOST:-https://freno.me}"
 NOOK_HOST="${NOOK_HOST:-https://nook.freno.me}"
 NESSA_HOST="${NESSA_HOST:-https://nessa.freno.me}"
 
@@ -43,6 +46,17 @@ fi
 
 echo
 echo "== live copy =="
+# The root is every other surface's entry point and deploys from the same tree, so it is
+# probed first. No -L: a redirect away from 200 is the failure we want to see, not a pass.
+root_code=$(curl -sS -o /dev/null -w '%{http_code}' "$ROOT_HOST/" 2>/dev/null)
+if [ "$root_code" = "200" ]; then
+  ok "$ROOT_HOST/ serves 200"
+elif [ -z "$root_code" ] || [ "$root_code" = "000" ]; then
+  bad "$ROOT_HOST/ gave no response, expected 200"
+else
+  bad "$ROOT_HOST/ returned $root_code, expected 200 (green subdomains do not cover the root)"
+fi
+
 page=$(curl -sS "$NOOK_HOST/" 2>/dev/null)
 case "$page" in
   *"One-click setup for Tailscale and authorized known hosts"*)