feat(web): public mesh stats counter + /api/public/stats endpoint

Live social-proof counter on the landing page, tied to the E2E
narrative. Formatted as understated mono footer, not hero brag.

Backend — new GET /api/public/stats (unauthed, 60s in-memory cache):
  {
    messagesRouted: SELECT COUNT(*) FROM mesh.message_queue,
    meshesCreated: SELECT COUNT(*) FROM mesh.mesh WHERE archivedAt IS NULL,
    peersActive: SELECT COUNT(*) FROM mesh.presence WHERE disconnectedAt IS NULL,
    lastUpdated: ISO timestamp,
  }

Aggregate counts only — no ids, no names, no ciphertext, no routing
metadata. Safe for public consumption. cache-control header sets
public/s-maxage=60 for edge caching. `x-cache: HIT|MISS` for debug.

Frontend — new MeshStats Server Component at
modules/marketing/home/mesh-stats.tsx. Reads the endpoint server-side
via the ~/lib/api/server client, renders monospace footer:

  ciphertext routed → 4,217 messages · 12 meshes · 8 peers online
  broker sees none of it

Graceful zero state: when messagesRouted === 0 shows
"ciphertext → ready to route" instead of embarrassing zeros. Tabular-
nums for the numeric spans so they don't jitter across renders.

Mounted between <CallToAction /> and <LatestNewsToaster />. Page-level
`export const revalidate = 60` so Next.js ISR refreshes the counter
every minute without a DB hit on every request (combined with the
API cache = two-layer 60s TTL, DB sees ~1 query/minute).

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

packages/api/src/schema/mesh-user.ts

@@ -186,6 +186,18 @@ export type GetMyMeshStreamResponse = z.infer<
   typeof getMyMeshStreamResponseSchema
 >;
 
+// ---------------------------------------------------------------------
+// Public stats (unauthed landing counter)
+// ---------------------------------------------------------------------
+
+export const publicStatsResponseSchema = z.object({
+  messagesRouted: z.number(),
+  meshesCreated: z.number(),
+  peersActive: z.number(),
+  lastUpdated: z.string(),
+});
+export type PublicStatsResponse = z.infer<typeof publicStatsResponseSchema>;
+
 export const getMyInvitesResponseSchema = z.object({
   sent: z.array(
     z.object({