I couldn't find information on this easily, so I thought it's worth putting this here.
The equivalent of drupal_var_export() / ctools_var_export() in Drupal 8/9 is Variable::export():
8.x
The D8 project I'm currently working on used the file-system based workflow for configuration management. As our deployment workflow improved and got slightly more complex, we started to run into issues with file permissions during deployments and wanted to revert back to the database based workflow that is the default for a new D8 installation.
During the Drupal 8 port of my relatively new Mefibs module I realized that block creation in code got somewhat more complex than it used to be in Drupal 7 and earlier. It took me quite a while to figure out how this works, especially because there is not a lot of documentation for Drupal 8 yet. So I had to dig my way through core to see how it's done there and finally I got around it. The following is a comparison between how we used to do this in Drupal 7 and how it's done in Drupal 8.