Recently working on my latest Drupal l9 project - BalticInvestors.com I faced a strange issue - after enabling the core default contact form, it seemed that data is not stored anywhere after actually filling out and submitting the webform.

Turns out there is a little helper module, which solves it - Contact Storage

Contact Storage module will provide storage for Contact messages which are fully-fledged entities in Drupal 8 and Drupal 9. This plus core contact module aims to provide functionality equivalent to the base-features of Webform or Entity Form.

Contact storage in Drupal 9

Contact storage in Drupal 9