This site has been created around 2007 with Drupal 6, upgraded to 7 a few years later. Now the time has come to upgrade again.
Oh, wait... you can't. Drupal 7 and 8 or 9 are fundamentally different so you'll have to migrate all data from the old Drupal 7 installation to the new Drupal 8 or 9 one. I went straight to Drupal 9.
The basic process was explained pretty clearly on this page: https://www.drupal.org/docs/upgrading-drupal/upgrade-using-web-browser