feat(ui): add new messages indicator button

ui/src/ui/app-render.ts

@@ -480,6 +480,8 @@ export function renderApp(state: AppViewState) {
                 onAbort: () => void state.handleAbortChat(),
                 onQueueRemove: (id) => state.removeQueuedMessage(id),
                 onNewSession: () => state.handleSendChat("/new", { restoreDraft: true }),
+                showNewMessages: state.chatNewMessagesBelow,
+                onScrollToBottom: () => state.scrollToBottom(),
                 // Sidebar props for tool output viewing
                 sidebarOpen: state.sidebarOpen,
                 sidebarContent: state.sidebarContent,

ui/src/ui/views/chat.ts

@@ -53,6 +53,9 @@ export type ChatProps = {
   // Image attachments
   attachments?: ChatAttachment[];
   onAttachmentsChange?: (attachments: ChatAttachment[]) => void;
+  // Scroll control
+  showNewMessages?: boolean;
+  onScrollToBottom?: () => void;
   // Event handlers
   onRefresh: () => void;
   onToggleFocusMode: () => void;
@@ -340,6 +343,20 @@ export function renderChat(props: ChatProps) {
           : nothing
       }
 
+      ${
+        props.showNewMessages
+          ? html`
+            <button
+              class="chat-new-messages"
+              type="button"
+              @click=${props.onScrollToBottom}
+            >
+              New messages ${icons.arrowDown}
+            </button>
+          `
+          : nothing
+      }
+
       <div class="chat-compose">
         ${renderAttachmentPreview(props)}
         <div class="chat-compose__row">