feat(analytics): record pageviews server-side only

Umami never received data: the client-side path (browser beacon to
/stats/api/send) has been dead in production. Pageviews are now
classified and recorded entirely on the server in the request proxy;
no tracking script ships to the browser anymore.

- Pure domain decision (decidePageview) filters real page views from
  assets, infrastructure paths, prefetches and bot user agents
- Pure payload builder maps facts onto the Umami send contract as an
  unnamed event, with the client identity travelling in headers
- proxy.ts wires request facts into the domain and fires the send
  without delaying the response; configured via UMAMI_WEBSITE_ID and
  UMAMI_API_ENDPOINT
- Removes the dead client analytics stack (components, adapters,
  /stats proxy route) and its layout mount

apps/web/src/analytics/recordPageviewToUmami.ts

@@ -0,0 +1,36 @@
+/**
+ * Imperative shell for page view analytics: sends one page view to the
+ * Umami collection API, identifying the visitor via request headers.
+ * Fire-and-forget by design — analytics must never delay a response.
+ */
+
+import type { PageviewFacts } from "@/src/domain/pageview-decision";
+import { buildUmamiPageviewBody } from "@/src/domain/umami-payload";
+
+const SEND_TIMEOUT_MS = 3_000;
+
+const websiteId = process.env.UMAMI_WEBSITE_ID ?? "";
+const apiEndpoint = (process.env.UMAMI_API_ENDPOINT ?? "").replace(/\/+$/, "");
+
+export function recordPageviewToUmami(facts: PageviewFacts): void {
+  if (!websiteId || !apiEndpoint) return;
+
+  const body = buildUmamiPageviewBody(facts, websiteId);
+
+  void fetch(`${apiEndpoint}/api/send`, {
+    method: "POST",
+    headers: {
+      "Content-Type": "application/json",
+      "User-Agent": facts.userAgent,
+      "X-Forwarded-For": facts.clientIp,
+      "Accept-Language": facts.language,
+    },
+    body: JSON.stringify(body),
+    signal: AbortSignal.timeout(SEND_TIMEOUT_MS),
+  }).catch((error: unknown) => {
+    console.error("umami pageview send failed", {
+      url: facts.url,
+      error: error instanceof Error ? error.message : String(error),
+    });
+  });
+}