feat: add new messages indicator style for chat interface

- Introduced a floating pill element above the compose area to indicate new messages.
- Styled the indicator with hover effects and responsive design for better user interaction.

ui/src/styles/chat/layout.css

@@ -100,6 +100,44 @@
   stroke-linejoin: round;
 }
 
+/* New messages indicator - floating pill above compose */
+.chat-new-messages {
+  align-self: center;
+  display: inline-flex;
+  align-items: center;
+  gap: 6px;
+  padding: 6px 14px;
+  margin: 8px auto;
+  font-size: 13px;
+  font-family: var(--font-body);
+  color: var(--text);
+  background: var(--panel-strong);
+  border: 1px solid var(--border);
+  border-radius: 999px;
+  cursor: pointer;
+  white-space: nowrap;
+  z-index: 10;
+  transition:
+    background 150ms ease-out,
+    border-color 150ms ease-out;
+}
+
+.chat-new-messages:hover {
+  background: var(--panel);
+  border-color: var(--accent);
+}
+
+.chat-new-messages svg {
+  width: 16px;
+  height: 16px;
+  stroke: currentColor;
+  fill: none;
+  stroke-width: 1.5px;
+  stroke-linecap: round;
+  stroke-linejoin: round;
+  flex-shrink: 0;
+}
+
 /* Chat compose - sticky at bottom */
 .chat-compose {
   position: sticky;