If you qualify as a fully vaccinated traveler, you don’t need a study permit to come to Canada to study for 6 months or less. However, getting a study permit when you don’t need one has benefits.
IRCC won’t request or look at your COVID-19 vaccination status when they process your application. A border services officer will make the final decision about whether you qualify as a fully vaccinated traveler.
You still need a valid travel document (electronic travel authorization or visitor visa) to come to Canada.