PHP PayPalでAPIを使って返金処理するには？

<?php
define('CLIENT_ID','｛ペイパルの管理画面のクライアントID｝');
define('APP_SECRET','｛ペイパルの管理画面のシークレット｝');
define('base','https://api-m.sandbox.paypal.com');
define('SELLER_PAYER_ID','｛販売者のメールアドレス｝');

$capture_id = "｛取引ID｝";
$amount = "｛返金額｝";

// APIリクエストの一意の識別子として使用されます。
// このヘッダーは、PayPalのサーバーに送信する各リクエストに一意のIDを付与するために使われ、
// トラッキングやデバッグの目的で便利です。
function generateUUID() {
  return sprintf(
    '%04x%04x-%04x-%04x-%04x-%04x%04x%04x',
    mt_rand(0,0xffff),
    mt_rand(0,0xffff),
    mt_rand(0,0xffff),
    mt_rand(0,0x0fff) | 0x4000,
    mt_rand(0,0x3fff) | 0x8000,
    mt_rand(0,0xffff),
    mt_rand(0,0xffff),
    mt_rand(0,0xffff)
  );
}

function base64url($data) {
  return rtrim(strtr(base64_encode($data),'+/','-_'),'=');
}

function getAuthAssertionValue() {
  $header = array(
    'alg' => 'none'
  );
  $encodedHeader = base64url(json_encode($header));
  $payload = array(
    'iss'      => CLIENT_ID,
    'payer_id' => SELLER_PAYER_ID,
  );
  $encodedPayload = base64url(json_encode($payload));
  return $encodedHeader.'.'.$encodedPayload.'.';
}

function generateAccessToken() {
  $url = base.'/v1/oauth2/token';
  $auth = base64_encode(CLIENT_ID.':'.APP_SECRET);

  $header = array(
    "Authorization: Basic {$auth}",
    'Accept: application/json',
    'Accept-Language: en_US',
  );
  $context = array(
    'http' => array(
      'method'  => 'POST',
      'header'  => implode("\r\n",$header),
      'content' => 'grant_type=client_credentials',
      'timeout' => 60, // second
    ),
  );
  $json = file_get_contents($url,false,stream_context_create($context));
  return json_decode($json)?->access_token;
}

$url = base."/v2/payments/captures/{$capture_id}/refund";
$accessToken = generateAccessToken();
$pay_pal_request_id = generateUUID();
$jwt = getAuthAssertionValue();

$header = [
  'Content-Type: application/json',
  "Authorization: Bearer {$accessToken}",
  "PayPal-Request-Id: {$pay_pal_request_id}",
  "PayPal-Auth-Assertion: {$jwt}",
];
$context = [
  'http' => [
    'method'  => 'POST',
    'header'  => implode("\r\n",$header),
    'content' => '{"amount":{"value":"'.$amount.'","currency_code":"JPY"}}',
    'timeout' => 60, // second
  ],
];
var_dump($context);

$json = file_get_contents($url,false,stream_context_create($context));
var_dump($json);