Persist state application on nextjs 13

[mmspring13]

Description

Description

I have same proble #496. But NextIntlClientProvider doesn’t helps for me.
If possible, I think it will be very useful to add a solution to this problem with one of the examples. For example, here example-app-router the problem is reproduced

Mandatory reproduction URL (CodeSandbox or GitHub repository)

https://github.com/amannn/next-intl/tree/main/examples/example-app-router

Reproduction description

Steps to reproduce:

1. Clone repo example-app-router
2. Create simple component like:

import { useState } from 'react'

function Cocoa() {
  const [count, setCount] = useState(0)
  const [name, setName] = useState('')

  return (
    <div
      style={{
        position: 'absolute',
        width: '600px',
        height: '200px',
        backgroundColor: 'orange',
        top: '40px',
        left: '40px',
        color: 'black',
        fontSize: '24px'
      }}
    >
      <button type='button' onClick={() => setCount(prev => prev += 1)}>
        +
      </button>
      <span>count {count}</span><br />
      <span>name {name}</span>
      <button type='button' onClick={() => setCount(prev => prev -= 1)}>
        -
      </button>
      <input
        type="text"
        value={name}
        onChange={
          e => setName(e.target.value)
        }
      />
    </div>
  );
}

export default Cocoa;

4. Use him on any page
5. Change language

Expected behaviour

the state and context are preserved

[github-actions]

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