Then apply to study German at a language school. That will get you a student permit for as long as your course lasts. You'll need to go back to Canada to apply and also to get a Type D (long term) visa to enter Switzerland again and you apply for the visa at the nearest Swiss embassy to your location. If the student permit is approved then the visa will be issued.
Another possibility would be to take a Masters course here as most are taught in English. It would also, theoretically, put you on the same footing as Swiss/EU nationals for job hunting once you graduate. https://www.bfm.admin.ch/bfm/en/home...abgaenger.html
Neither of these will allow you to extend your current stay here though. You will need to go back to Canada and take things from there.
Something else to consider - what exactly is your Swiss connection and could you claim Swiss citizenship because of it? https://www.bfm.admin.ch/bfm/en/home...uergerung.html
That would get over the non-EU nationality problem and allow you to apply as a Swiss national for any job you want to.