I'm reasonably sure that the information on your myCIC account regarding the background check is usually wrong.
Specifically, based on GCMS notes from a bunch of applicants here, the background check is initiated rather early in the process.
This makes sense since it takes quite a long time but causes little work to IRCC since they just submit some requests to the agencies.
The medical requests are issued on a rather inconsistent basis. Usually 3-4 months after AOR, sometimes way later.
Again this step causes little work for IRCC. The only guideline there is that the medical needs to be valid at the time of landing. Medicals are valid for one year I believe, so they would not make the request too, too early in the process to avoid the having the applicant being required to take a medical exam again.
The eligibility review causes by far the most work as some officer actually needs to read your entire application with all supporting documents and letters of explanation. As we all know this is A LOT of paperwork to go through.
Hence this is generally the last step as they likely operate on a first received-first processed basis (roughly).
Sometimes this gets jumbled up. I know June applicants (I am one) got their medical requests incredibly late. The reason? Anyone's guess. I therefore received AIP before my medical was even submitted. There's a good possibility, that if I had done my medical on a standard timeline, I'd be at DM now.
Anyway, it seems processing times generally have gone way down over the last year, and that might have caused some timelines to be non-standard.
I bet requiring the Schedule A and police clearance upfront is a big reason for the reduced processing times, as it eliminates an entire step in the process.