No. That's not the way to read it. I can commend to you my book from 2021, Governing Canada, which sets this out in some detail.
The Privy Council Office is the Prime Minister's department. The Prime Minister has seven distinct hats and roles in government. Chair of cabinet is one, first minister in the federation is another, international leader for the purposes of dealing with other countries is another, and so on. The Privy Council Office is a set of secretariats and teams that support those seven roles. One of them is the security and intelligence branch.