The application guide outlines the process, including all the routine steps and some information about possible additional steps (like being asked for more information). This information follows the subheading "Processing your application" which is part of "Step 6 - Submit your application."
That is a very general outline of the process, and each of the steps referenced has been discussed in depth in numerous threads in this forum. For example, Step 7 is barely two lines about preparing for the test, but you can find many topics in this forum in which preparing for the test, what to expect at the test, and related information, is discussed in depth.
Step 8 discusses actually going to the interview and test. Here too, there are scores of in-depth discussions about this step in this forum.
Additionally, there are numerous Program Delivery Instructions (PDIs) which provide further information about the various steps in citizenship application processing.
Many of these are grouped together under the heading "Citizenship decision-making" which can be found here:
https://www.canada.ca/en/immigration-refugees-citizenship/corporate/publications-manuals/operational-bulletins-manuals/canadian-citizenship/admininistration/decisions.html
Many of the links from that page go to a specific PDI, such as the one about interviewing adult applicants, which can be found here:
https://www.canada.ca/en/immigration-refugees-citizenship/corporate/publications-manuals/operational-bulletins-manuals/canadian-citizenship/admininistration/decisions/interviewing-adult-applicants.html
That PDI is just an example. There are many PDIs.
And, again for just one example, the information found in the PDI about interviewing adult applicants is also discussed in-depth in numerous topics in this forum. And similarly for most of the pieces of the puzzle, from basic decision-making procedures, to who and why someone is referred for a hearing with a Citizenship Judge, there are related topics in this forum.
Along the way, parallel to the processing of the application by IRCC processing agents, background checks are referred to the RCMP and CSIS, for criminality and security issues respectively. These are routine, mostly confidential/secret (meaning the public is given very little information about these procedures), but more thorough than a mere name-record check (the IRCC GCMS background checks, which are done multiple times during the processing, include a criminal history name-record check apart from the RCMP background check). Here too, this subject is discussed extensively in many topics in this forum.
Overall, all adult applications go through the following:
CPC-Sydney procedures:
-- Completeness check (assures application meets minimum requirements for processing . . . not requirements for citizenship, but requirements for processing a citizenship application)
-- GCMS check (last information we have about this is that this is repeated every time an action is taken on the application)
-- referrals to RCMP and CSIS for criminality and security clearances, respectively
-- Triage screening prior to referral to local office (probable this still happens but we are not certain; identifies applicants to be given RQ or other requests for additional information or documents)
Local Office procedures:
-- Local office processing agent preparation for interview and testing
-- Interview and test (test as applicable)
-- Citizenship Officer review and decision
-- Oath
There are additional steps or actions that can occur during the process, including:
-- selection for Quality Assurance Exercise (pursuant to which applicant is required to provide additional information and documentation)
-- Finger Print requests
-- update of or additional criminal history or security background checks
-- additional information or document requests, including RQ-lite (CIT 0520) or full-blown RQ (CIT 0171)
-- -- these can happen following AOR, prior to interview/test, at the interview, or following the interview
-- referral for in-person hearing with Citizenship Officer (we see almost no reports of this but IRCC information and the Citizenship Act provide for this procedure in some cases)
-- referral for review and hearing with Citizenship Judge (if IRCC concludes applicant did not meet physical presence requirement, case goes to a Citizenship Judge)
All of these are the subject of multiple discussions in this forum.