feat(chat): add manual refresh for delivered agents

src/pages/Chat/TeacherIntroduction.tsx

@@ -1,6 +1,6 @@
 import * as Tooltip from '@radix-ui/react-tooltip';
 import { Sparkles } from 'lucide-react';
-import type { ReactElement, Ref } from 'react';
+import { useRef, type ReactElement, type Ref } from 'react';
 import type { TeacherDefinition } from '../../../shared/coding-teacher';
 import { TeacherAvatar } from './TeacherAvatar';
 
@@ -13,11 +13,23 @@ export function TeacherIntroduction({ definition, children, contentRef, open, on
   onOpenChange(open: boolean): void;
 }) {
   const description = definition?.description?.trim();
-  return <Tooltip.Root open={Boolean(description) && open} onOpenChange={onOpenChange}>
+  const clicked = useRef(false);
+  return <Tooltip.Root open={Boolean(description) && open} onOpenChange={(next) => {
+    if (!next || !clicked.current) onOpenChange(next);
+  }}>
     <Tooltip.Trigger asChild onPointerEnter={(event) => {
       // Adjacent entries must switch immediately, even inside the previous
       // tooltip's pointer grace area used when moving into its readable card.
-      if (event.pointerType !== 'touch') onOpenChange(true);
+      if (event.pointerType === 'touch') return;
+      if (event.relatedTarget instanceof Node && event.currentTarget.contains(event.relatedTarget)) return;
+      clicked.current = false;
+      onOpenChange(true);
+    }} onClick={() => {
+      // A delayed Radix hover callback must not reopen the card after selection.
+      clicked.current = true;
+      onOpenChange(false);
+    }} onFocus={() => {
+      clicked.current = false;
     }} onPointerMove={(event) => {
       // pointerEnter owns hover opening. Skip Radix's second opening path so
       // moving inside an entry after clicking it cannot reopen its introduction.