There is a API token priv for wp-toolkit but there is nothing in any of the several places the API is documented that it is referenced.
Screenshots are accessible via:
https://$host:2087/$session/cgi/wpt/index.php?action=/screenshot/id/$num?v=$ver
Presumably $num is site ID within wp-toolkit. $ver is purely for cache busting/versioning.
It would be great to see a unified/updated API doc interface for cPanel - it's grown into quite the spaghetti monster over the years.