feat(auth): implement all 16 homepage/login/register review items

- add countArticles() (published-only, mirrors news-list) and warm total_articles
- localize homepage metadata; bind articleCount to both stats; unique photo alts
- drop duplicate news date and the mascot preload priorities
- extract shared AuthPageFrame/AuthUsersCards used by /login and /register
- login: localized noindex metadata, session redirect via safeRedirectPath,
  ?from passthrough from proxy, unified auth roster cache keys, registered notice
- register: localized metadata, session redirect to /me, unified cache keys
- add resend-verification flow on /verify with rate-limited non-enumerable action
- add safeRedirectPath() with unit tests
- register form: live requirements checklist + password mismatch guard
- login form: unverified state with resend-link CTA
- honour prefers-reduced-motion in TypewriterText
- add 6 translations across all 25 locales

src/lib/services/public-counters.ts

@@ -1,7 +1,7 @@
 import "server-only";
 
-import { count, eq } from "drizzle-orm";
-import { CameraWeb, db, Rooms, User } from "@/lib/db";
+import { and, count, eq, or, sql } from "drizzle-orm";
+import { CameraWeb, db, Rooms, User, WebsiteArticles } from "@/lib/db";
 
 /**
  * Row counters for the public homepage.
@@ -40,6 +40,27 @@ export async function countPhotos(): Promise<number> {
 	return row?.total ?? 0;
 }
 
+/**
+ * Published articles only — the same filter `getNewsList` renders from, so the
+ * "Articles" figure on the homepage can never disagree with the news section
+ * that sits next to it.
+ */
+export async function countArticles(): Promise<number> {
+	const [row] = await db
+		.select({ total: count() })
+		.from(WebsiteArticles)
+		.where(
+			and(
+				eq(WebsiteArticles.status, "published"),
+				or(
+					sql`${WebsiteArticles.publishAt} IS NULL`,
+					sql`${WebsiteArticles.publishAt} <= NOW()`,
+				),
+			),
+		);
+	return row?.total ?? 0;
+}
+
 /**
  * Online users is deliberately *not* estimated: it is read from an index over a
  * small subset of rows, it is the one counter people watch closely, and being a