Dev tools cannot connect to my project with Apollo client and Next.js

When refreshing the Next.js page, Apollo client dev tools cannot connect to my Apollo client. I have `connectToDevTools` enabled in the client.

### Link to Reproduction

```ts
import { ApolloClient, InMemoryCache } from '@apollo/client'

export const client = new ApolloClient({
uri: 'https://graphqlplaceholder.vercel.app/graphql',
cache: new InMemoryCache(),
connectToDevTools: true,

name: 'apollo-client-dev',
version: '1.3',
queryDeduplication: false,
defaultOptions: {
watchQuery: {
fetchPolicy: 'cache-and-network',
},
},
})
```

```tsx
'use client'

import { Button } from '@/components/ui/button'
import { gql, useMutation, useQuery } from '@apollo/client'

const CREATE_POST = gql`
mutation CreatePost {
createPost(post: { userId: 1, title: "title", body: "body" }) {
id
title
body
}
}
`

const GET_POSTS = gql`
query GetPosts {
posts {
id
title
body
}
}
`

type Post = {
id: number
title: string
}

const Home = () => {
const { loading, error, data } = useQuery(GET_POSTS)
const [addPost, { data: mutationData }] = useMutation(CREATE_POST, {
update(cache, { data: { addPost } }) {
cache.modify({
fields: {
posts(existingPosts = []) {
const newPostRef = cache.writeFragment({
data: addPost,
fragment: gql`
fragment NewPost on Post {
id
text
completed
}
`,
})
return [...existingPosts, newPostRef]
},
},
})
},
})

if (loading) return 'Loading...'
if (error) return `Error! ${error.message}`

return (

export default Home
```

### `@apollo/client` version

^3.13.8

### Apollo Client Devtools version
4.18.15 (Firefox)

Start with the supplied Apollo client setup and the Next.js Home component, using @apollo/client ^3.13.8 and Apollo Client Devtools 4.18.15 in Firefox. Reproduce a page refresh with connectToDevTools enabled and verify that the devtools reconnects to the Apollo client afterward.

Written by the indexing model from the issue text.