fix: float teacher introductions above a centered welcome

src/pages/Chat/CodingChatBody.tsx

@@ -8,19 +8,18 @@ export function CodingChatBody({ welcome, hidden, bubble, children }: {
   useLayoutEffect(() => {
     const body = ref.current;
     const content = body?.querySelector<HTMLElement>('.classroom-chat-view');
-    if (!body || !content || hidden || !bubble) return;
+    if (!body || !content || !welcome || hidden || !bubble) return;
     const update = () => {
       const area = body.getBoundingClientRect();
       const message = bubble.getBoundingClientRect();
       const overlaps = message.height > 0 && message.right > area.left && message.left < area.right && message.bottom > area.top;
-      const rightInset = Math.ceil(area.right - message.left + 24);
-      const besideTeacher = overlaps && area.width >= 900 && area.width - rightInset - 24 >= 420;
-      // Reserve the same right rail for the welcome and bottom input. The teacher keeps its own fixed width.
-      body.style.paddingLeft = besideTeacher ? '24px' : '';
-      body.style.paddingRight = besideTeacher ? `${rightInset}px` : '';
-      // Put compact-screen clearance inside the scrolling heading, never around the fixed bottom input.
-      content.style.setProperty('--teacher-top-inset', welcome && overlaps && !besideTeacher
-        ? `${Math.max(0, Math.ceil(message.bottom - content.getBoundingClientRect().top))}px` : '0px');
+      // The teacher floats over the page; it never narrows or shifts the main column.
+      // Only compact screens need scrollable space to reveal the welcome below the overlay.
+      if (overlaps && area.width < 900) {
+        content.style.setProperty('--teacher-top-inset', `${Math.max(0, Math.ceil(message.bottom - content.getBoundingClientRect().top + 24))}px`);
+      } else {
+        content.style.removeProperty('--teacher-top-inset');
+      }
     };
     update();
     const observer = typeof ResizeObserver === 'undefined' ? null : new ResizeObserver(update);
@@ -28,7 +27,6 @@ export function CodingChatBody({ welcome, hidden, bubble, children }: {
     window.addEventListener('resize', update);
     return () => {
       observer?.disconnect(); window.removeEventListener('resize', update);
-      body.style.paddingLeft = ''; body.style.paddingRight = '';
       content.style.removeProperty('--teacher-top-inset');
     };
   }, [welcome, hidden, bubble]);