OK, try this, to get a list of the assignment plugin names on your installation:
select distinct plugin from mdl_assign_plugin_config;
Identify the name of the assignment plugin you want, and try this:
select a.name, c.shortname from mdl_assign_plugin_config apc
join mdl_assign a on a.id = apc.assignment
join mdl_course c on c.id = a.course
where apc.plugin = <your_plugin>;
This should give you a list of the assignment names and course shortnames where the plugin of your choice is active. (It won't tell you if a student has actually submitted an assignment of this type; that needs something different.).
Let me know how you get on.