It does say on their official site that no authorisation is required for accompanying immediate family member. If needed, print out thier webpage to show to border officerits better to obtain written authorization just in case. i’ve personally spoken to embassy staff in my country and to CBSA agents. The embassy staff said that the written authorization isn’t required, but the CBSA agents said that it is. make of that what you will
Also, getting authorisation takes a while and you are not guaranteed to get an answer. I have a friend who needs to go meet her husband in Canada and has applied for authorisation since April - still waiting even after sending multiple webforms.
From CIC's website updated on July 14th 2021 ( https://travel.gc.ca/travel-covid/travel-restrictions/visitors-workers-students#students):
If immediate family members want to be with you in Canada
They don’t need a written authorization from IRCC to travel with you. However, they must show that their reasons for travel are non-discretionary (non-optional). For example, they’ll help you get established and support you in Canada.
If your immediate family member will study or work in Canada
You must submit all of your applications together when you apply online.
If they won’t study or work
They may still need an electronic travel authorization (eTA) or a visitor visa to travel to Canada.
If they need a visitor visa, you should include their application when you apply online for your study permit.
If they need an eTA, they must apply for one separately.