Thanks for your response. My eligibility is "recommend passed" and the latest update based on the GCMS notes that I got a week ago was in April when the eligibility was reviewed by a case processing agent and they recommend passed. So, no officer has yet looked at the case. and the note about background check has been the same in my online profile since the beginning, and never changed to "we are processing your background check".
@legalfalcon do you think I can do anything to speed up processing? Should I ask for any specific information in webforms or when I call IRCC?