Export the default system email text to code? Is it possible to move the default system email message text found in the account settings page out of the database and into the code for version control?

Currently using the mimemail module since we use HTML/CSS formatted emails.
Settings in files for version control was one of the biggest changes in the 7 -> 8 jump. Drupal 7 has no built-in way to do it. You may wish to see How to version control data stored in mysql.

If you want Drupal-specific tool, investigate Configuration Management module: 


  The configuration management module enables the ability to keep track of specific configurations on a Drupal site, provides the ability to move these configurations between different environments (local, dev, qa, prod), and also move configurations between completely different sites (migrate configurations) without the use of modules with all configuration being owned by the site.