Компонент Shadecdn/ui Drawer внутри div

1. В components/ui/drawer.tsx замените fixed className в <DrawerOverlay /> и <DrawerContent /> на absolute.

2. Не рендерить <DrawerPortal>. измените строку 31, 44 с <DrawerPortal> на <>.

3. При рендеринге ящика укажите родительский <Chat />relative className.

export default function Page() {
  return (
    <div className = "min-h-screen flex justify-center items-center">
      <div className = "size-96 bg-sky-300 relative overflow-hidden">
        <Drawer>
          <DrawerTrigger>Trigger</DrawerTrigger>
          <DrawerContent>
            Content
          </DrawerContent>
        </Drawer>
      </div>
    </div>
  )
}

components/ui/drawer.tsx:

'use client';

import * as React from 'react';
import { Drawer as DrawerPrimitive } from 'vaul';

import { cn } from "@/lib/utils";

const Drawer = ({ shouldScaleBackground = true, ...props }: React.ComponentProps<typeof DrawerPrimitive.Root>) => (
  <DrawerPrimitive.Root shouldScaleBackground = {shouldScaleBackground} {...props} />
);
Drawer.displayName = 'Drawer';

const DrawerTrigger = DrawerPrimitive.Trigger;

const DrawerPortal = DrawerPrimitive.Portal;

const DrawerClose = DrawerPrimitive.Close;

const DrawerOverlay = React.forwardRef<
  React.ElementRef<typeof DrawerPrimitive.Overlay>,
  React.ComponentPropsWithoutRef<typeof DrawerPrimitive.Overlay>
>(({ className, ...props }, ref) => (
  <DrawerPrimitive.Overlay ref = {ref} className = {cn('absolute inset-0 z-50 bg-black/80', className)} {...props} />
));
DrawerOverlay.displayName = DrawerPrimitive.Overlay.displayName;

const DrawerContent = React.forwardRef<
  React.ElementRef<typeof DrawerPrimitive.Content>,
  React.ComponentPropsWithoutRef<typeof DrawerPrimitive.Content>
>(({ className, children, ...props }, ref) => (
  <>
    <DrawerOverlay />
    <DrawerPrimitive.Content
      ref = {ref}
      className = {cn(
        'absolute inset-x-0 bottom-0 z-50 mt-24 flex h-auto flex-col rounded-t-[10px] border bg-background',
        className,
      )}
      {...props}
    >
      <div className = "mx-auto mt-4 h-2 w-[100px] rounded-full bg-muted" />
      {children}
    </DrawerPrimitive.Content>
  </>
));
DrawerContent.displayName = 'DrawerContent';

const DrawerHeader = ({ className, ...props }: React.HTMLAttributes<HTMLDivElement>) => (
  <div className = {cn('grid gap-1.5 p-4 text-center sm:text-left', className)} {...props} />
);
DrawerHeader.displayName = 'DrawerHeader';

const DrawerFooter = ({ className, ...props }: React.HTMLAttributes<HTMLDivElement>) => (
  <div className = {cn('mt-auto flex flex-col gap-2 p-4', className)} {...props} />
);
DrawerFooter.displayName = 'DrawerFooter';

const DrawerTitle = React.forwardRef<
  React.ElementRef<typeof DrawerPrimitive.Title>,
  React.ComponentPropsWithoutRef<typeof DrawerPrimitive.Title>
>(({ className, ...props }, ref) => (
  <DrawerPrimitive.Title
    ref = {ref}
    className = {cn('text-lg font-semibold leading-none tracking-tight', className)}
    {...props}
  />
));
DrawerTitle.displayName = DrawerPrimitive.Title.displayName;

const DrawerDescription = React.forwardRef<
  React.ElementRef<typeof DrawerPrimitive.Description>,
  React.ComponentPropsWithoutRef<typeof DrawerPrimitive.Description>
>(({ className, ...props }, ref) => (
  <DrawerPrimitive.Description ref = {ref} className = {cn('text-sm text-muted-foreground', className)} {...props} />
));
DrawerDescription.displayName = DrawerPrimitive.Description.displayName;

export {
  Drawer,
  DrawerPortal,
  DrawerOverlay,
  DrawerTrigger,
  DrawerClose,
  DrawerContent,
  DrawerHeader,
  DrawerFooter,
  DrawerTitle,
  DrawerDescription,
};

Вот и все. Возможно, вам придется изменить некоторые стили в соответствии с вашим вариантом использования.