Split Settings into sub-pages and add DNS cache clearing

Settings was a single long page. Break it into a sub-nav (Notifications,
DNS Badges, Cache) with its own route per section, each loading and
saving independently. Also add the DNS record-cache clearing action
that Sloth Manager had — a new admin-only POST /api/dns/cache/clear
truncates the zone/record cache tables so stale data can be wiped and
zones re-synced from scratch.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

web/src/pages/settings/CacheSettings.tsx

@@ -0,0 +1,47 @@
+import { useState } from "react";
+import { api } from "../../api/client";
+
+export default function CacheSettings() {
+  const [clearing, setClearing] = useState(false);
+  const [cleared, setCleared] = useState(false);
+  const [error, setError] = useState<string | null>(null);
+
+  async function handleClear() {
+    if (!confirm("Clear the DNS record cache? All zones will need to be re-synced afterwards.")) return;
+    setClearing(true);
+    setError(null);
+    setCleared(false);
+    try {
+      await api.dns.clearCache();
+      setCleared(true);
+      setTimeout(() => setCleared(false), 3000);
+    } catch (err) {
+      setError(err instanceof Error ? err.message : String(err));
+    } finally {
+      setClearing(false);
+    }
+  }
+
+  return (
+    <>
+      <h3 className="mb-3">Cache</h3>
+      <div className="card">
+        <div className="card-header">
+          <h3 className="card-title">DNS record cache</h3>
+        </div>
+        <div className="card-body">
+          <p className="text-secondary">
+            The DNS module keeps a local copy of every synced zone and record so pages load instantly. Clear it if
+            you see stale or incorrect data — every zone will need to be re-synced from its provider afterwards.
+          </p>
+          {error && <div className="alert alert-danger">{error}</div>}
+        </div>
+        <div className="card-footer">
+          <button className="btn btn-danger" onClick={handleClear} disabled={clearing}>
+            {clearing ? "Clearing…" : cleared ? "✓ Cache cleared" : "Clear DNS Cache"}
+          </button>
+        </div>
+      </div>
+    </>
+  );
+}