Module incompatible with Bigpipe

I noticed the following error on php logs each time a user tried to log in.

RuntimeException: Failed to start the session because headers have already been sent by "/var/www/html/vendor/symfony/http-foundation/Response.php" at line 426. in Symfony\Component\HttpFoundation\Session\Storage\NativeSessionStorage->start() (line 132 of /var/www/html/vendor/symfony/http-foundation/Session/Storage/NativeSessionStorage.php)
#0 /var/www/html/web/core/lib/Drupal/Core/Session/SessionManager.php(144): Symfony\Component\HttpFoundation\Session\Storage\NativeSessionStorage->start()
#1 /var/www/html/web/core/lib/Drupal/Core/Session/SessionManager.php(109): Drupal\Core\Session\SessionManager->startNow()
#2 /var/www/html/vendor/symfony/http-foundation/Session/Session.php(59): Drupal\Core\Session\SessionManager->start()
#3 /var/www/html/web/core/modules/big_pipe/src/Render/BigPipe.php(240): Symfony\Component\HttpFoundation\Session\Session->start()
#4 /var/www/html/web/core/modules/big_pipe/src/Render/BigPipe.php(295): Drupal\big_pipe\Render\BigPipe->performPreSendTasks()
#5 /var/www/html/web/core/modules/big_pipe/src/Render/BigPipeResponse.php(112): Drupal\big_pipe\Render\BigPipe->sendContent(Object(Drupal\big_pipe\Render\BigPipeResponse))
#6 /var/www/html/vendor/symfony/http-foundation/Response.php(423): Drupal\big_pipe\Render\BigPipeResponse->sendContent()
#7 /var/www/html/web/index.php(20): Symfony\Component\HttpFoundation\Response->send()
#8 {main}

I would say its due to Drupal core 9.2 changes that many other modules have faced. Attached a patch that fixes the error, but I still get the X-Cacheable:Cookie in the response header. Not sure if this still requires adjusting the default.vcl template.