I'm reading the docs on server actions right now and I'm a little confused. Do server actions get sent to the client as part of the bundle?

For example, if I have this:

1.

// actions.ts
'use server';

import prisma from '@/lib/prisma';

export async function handleClick() {
  return await prisma.post.delete({
    where: {
      id: 1,
    },
  });
}

// page.tsx
import { handleClick } from '@/actions/actions';

export default function Page() {
  return (
    <div>
      <h1>Home page</h1>
      <button
        onClick={handleClick}
      >
        Button
      </button>
    </div>
  );
}

Would Page include the server action in the bundle?

2. What if you inline the server action? Does it get sent in the bundle then?

// page.tsx
import prisma from '@/lib/prisma';

export default function Page() {
  return (
    <div>
      <h1>Home page</h1>
      <button
        onClick={async () => {
          'use server'
          await prisma.post.delete({
            where: {
              id: 1,
            }
          })
        }}
      >
        Button
      </button>
    </div>
  );
}