Ugh! Yes, course copy is broke ... depending upon the original course and factors related to hosting.
Is your moodle selfhosted? Is hosting shared hosting? ...
Moodle version is? Are you admin of the moodle? Do you have shell access to your server?
I ask the questions above because fixing the issue might require more than the GUI.
IF you are admin, go to Courses and the Category where the copy was to be saved. Look at the bottom of the course list ... do you see something like 'Pending ... blah, blah'? Do you see a trash can in that course row? Try the trash can icon. That might not work, BTW.
Do you have a panel - like cPanel and can browse files? if so, look in moodledata/temp/backup/ for long directory names with a date/time stamp of 24 hours ago. You can delete that.
Then there is your cron job ... is it running as it should? The stuck job might be an adhoc task now to try again later ... doing something about that does require command line access to the site.
You are better off making a no user backup and might even deselect modules first. Then do a restore of that no user/selected modules backup to a new course in whatever category.
'SoS', Ken