Hi,
I am May 23 and stuck in Background NA stage.
The Background check starts automatically 1-7 days after your Medical Passed, so the fact that your Background check in MyCic account is still shown as if they havent started it yet, is incorrect, especially if you passed your medical exam a month ago.
Since the update of the online system in February, you cannot rely much on what is written on your MyCic account, particularly for Background check.
Many times your account doesnt reflect at what stage your application is. For example, if you check signatures of other applicants, who recently got their PPRs, you will see that majority of them, didnt have any updates after "Medical passed" at all, and received PPRs while their Background check showed "Not applicable", "Not started" etc.
If you really want to know what is happening with your application, I'd suggest you send an e-mail to Ottawa
CPC-CTD-Ottawa@cic.gc.ca and inquire about the status of your application