I decide to provide a data point here, in case useful to some folks.
I applied last year but decided to withdraw (I posted a separate thread on this forum before) because I missed one trip abroad. Fast forward, I applied again.
My timeline is exactly as reported here as some other folks did: BG check passed, citizenship test passed, etc. However, I see those other folks getting LPP completed while mine is not. From the ATIP notes that I read, it was the same day that IRCC asked me for an interview through Microsoft Teams as other people were getting LPP completed.
Therefore, I guess that some junior clerk would go through all the applications, approve the trivial ones, and hand them over for an interview by a senior officer. However, the interview was backlogged too much, and I waited for 40 days before I received an interview notice, I finally got an interview about two months after IRCC decided to interview me.
Then I had an interview with the IRCC officer the other day. The officer said that the only reason that I got interviewed was that I had applied and withdrawn before. All the other criteria are good: 5 years of taxes, continuous work experience, and a lot more than the required physical presence -- due to my first miscalculation, my physical presence is well above 1095.
The interview was short (about 3 mins), and the officer said that she would expect me to get an oath notice very soon. I'm still waiting, and hope the oath ceremony will be soon.
Takeaway: 1) the backlog is real, especially when it comes to interviews or senior officers. 2) I don't think ATIP notes have accelerated anything, as I see my timeline as similar to those who required ATIP notes every week. 3) please double and triple-check your travel history before submission. You can see that even though my case is simple, a withdrawal on file did slow down my process significantly.