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There is one thing what I noticed and experienced that once you filed a mandamus then there is chances that your file touched by someone and it starts moving. So, in my case I spent $4200 up to the Memorandum of Argument stage. Then I discontinued this year January, and once I received the GCMS notes later, where I noticed under the "Security Sub Activities Section ": Security Favorable, date created on March. Then in July my Comprehensive Security marked as completed. Now a week ago I also received Portal 1 email. And my expired medical also extended by IRCC.

Think that was pure coincidence. Just filing a writ of mandamus typically does not lead to any movement of your application.