Issue with DocuSign sending Envelopes

I recently changed my DocuSign integration to use the JWT OAuth flow. To achieve this I have a few classes.

OAuth Client

<?php
namespace App\DocuSign;

use DocuSign\eSign\Client\ApiClient;
use DocuSign\eSign\Client\Auth\OAuth;
use DocuSign\eSign\Configuration;
use Exception;
use Illuminate\Support\Facades\Log;

/**
 * Helper class to generate a DocuSign Client instance using JWT OAuth2.
 *
 * @see
 *
 */
class OAuthClient
{
    /**
     * Create a new DocuSign API Client instance using JWT based OAuth2.
     */
    public static function createApiClient()
    {
        $config = (new Configuration())->setHost(config('docusign.host'));
        $oAuth = (new OAuth())->setOAuthBasePath(config('docusign.oauth_base_path'));

        $apiClient = new ApiClient($config, $oAuth);

        try {
            $response = $apiClient->requestJWTUserToken(
                config('docusign.integrator_key'),
                config('docusign.user_id'),
                config('docusign.private_key'),
                'signature impersonation',
                60
            );

            if ($response) {
                $accessToken = $response[0]['access_token'];

                $config->addDefaultHeader('Authorization', 'Bearer ' . $accessToken);

                $apiClient = new ApiClient($config);

                return $apiClient;
            }
        } catch (Exception $e) {
            // If consent is required we just need to give the consent URL.
            if (strpos($e->getMessage(), 'consent_required') !== false) {
                $authorizationUrl = config('docusign.oauth_base_path') . '/oauth/auth?' . http_build_query([
                    'scope' => 'signature impersonation',
                    'redirect_uri' => config('docusign.redirect_url'),
                    'client_id' => config('docusign.integrator_key'),
                    'response_type' => 'code'
                ]);

                Log::critical('Consent not given for DocuSign API', [
                    'authorization_url' => $authorizationUrl
                ]);

                abort(500, 'Consent has not been given to use the DocuSign API');
            }

            throw $e;
        }
    }
}

Signature Client Service

<?php
namespace App\DocuSign;

use DocuSign\eSign\Api\EnvelopesApi;
use DocuSign\eSign\Client\ApiClient;

class SignatureClientService
{
    /**
     * DocuSign API Client
     */
    public ApiClient $apiClient;

    /**
     * Create a new instance of our class.
     */
    public function __construct()
    {
        $this->apiClient = OAuthClient::createApiClient();
    }

    /**
     * Getter for the EnvelopesApi
     */
    public function getEnvelopeApi(): EnvelopesApi
    {
        return new EnvelopesApi($this->apiClient);
    }
}

Then, in my constructors where I want to use it I'm doing

/**
 * Create a new controller instance
 */
public function __construct()
{
    $this->clientService = new SignatureClientService();
    $this->envelopesApi = $this->clientService->getEnvelopeApi();
}

Finally, I use it like so

$envelopeSummary = $this->envelopesApi->createEnvelope(config('docusign.api_account_id'), $envelopeDefinition);

But I get an error that reads

DocuSign\eSign\Client\ApiException: Error while requesting server, received a non successful HTTP code [400] with response Body: O:8:"stdClass":2:{s:9:"errorCode";s:21:"USER_LACKS_MEMBERSHIP";s:7:"message";s:60:"The UserID does not have a valid membership in this Account.";} in /homepages/45/d641872465/htdocs/sites/ita-portal/vendor/docusign/esign-client/src/Client/ApiClient.php:344

I researched this and this would imply that the user is not within the account, but they are. I also checked that this account owns the envelopes that I'm trying to send.

For reference I took inspiration for envelope sending from here: https://developers.docusign.com/docs/esign-rest-api/how-to/request-signature-template-remote/