I have a resonable understanding of PNR management given my professional background. In a simplified way, here's what's happening:
When an airline agent (human or digital) tries to check a passenger in for a flight to Canada (or the US or many other countries), it must submit the passport / citizenship information to the destination country's authorities. The data is added to the PNR and the PNR is submitted. The destination country's system then sends back an "ok to board" message.* Only once that message is received can a boarding pass be issued and a passenger board the aircraft. You can sometimes see a remark "DOCOK" or "ADOC" on your boarding pass. The passport data stays in the PNR and the PNR can also be accessed by the governments of the departing country (or Schengen zone), transiting countries, and probably many others more (including the US on almost all itineraries).
For flights to Canada, the Canadian ETA system will not issue ETAs for non-Canadian passports held by individuals identified as being Canadian citizens. Therefore, Canadian citizens cannot use a passport that requires an ETA to board a flight to Canada. The only passports not requiring an ETA are Canadian and American. Which leads to the conclusions described in the FAQ above: As a Canadian citizen, you must use a Canadian or US passport to board a flight to Canada. And that data is visible to all governments somehow affected by this PNR.
Note: A PNR includes all segments of a ticket. So if you book FRA-IST-YYZ on one ticket, and add your Canadian citizenship in IST to obtain the boarding pass to YYZ, it is still stored in the PNR to which the Schengen / German authorities have access.
As I wrote upthread, if and to what degree Schengen countries go comb through this massive heap of data, track it back to their citizens, screen for dual citizenship violations, and then take action against them, is a completely different subject.
*In the absence of the ok from the destination country, you may sometimes get a "this is not a boarding pass - your documents must be inspected at the gate" type of document that allow you to go as far as the departure gate where the trained agents sit, but not on board.