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/api/client.ts

@@ -473,6 +473,7 @@ export const api = {
           { method: "DELETE" },
         ),
     },
+    clearCache: () => request<{ ok: true }>("/api/dns/cache/clear", { method: "POST" }),
   },
   servers: {
     list: () => request<{ servers: ServerRecord[] }>("/api/servers"),