Quick chat FAB, active session indicators, memory tab counts, improved new session

app/page.tsx

@@ -1,7 +1,7 @@
 "use client";
 
 import Link from "next/link";
-import { Puzzle, Timer, Sparkles, Settings } from "lucide-react";
+import { Puzzle, Timer, Sparkles, Settings, MessageCircle } from "lucide-react";
 import { useQueryClient } from "@tanstack/react-query";
 import { StatusCard } from "@/components/StatusCard";
 import { StatsCard } from "@/components/StatsCard";
@@ -66,6 +66,15 @@ export default function PulsePage() {
           </div>
         )}
       </div>
+
+      {/* Quick chat FAB */}
+      <Link
+        href="/history/new"
+        className="fixed right-5 z-40 flex items-center justify-center w-14 h-14 rounded-full shadow-lg active:scale-90 transition-transform"
+        style={{ background: "var(--accent)", bottom: "calc(5.5rem + var(--safe-bottom))" }}
+      >
+        <MessageCircle size={22} color="white" />
+      </Link>
     </div>
   );
 }