Yes, you can apply for a student visa and a spouse visa in Canada at the same time, although it is not recommended. You should, in my view, apply for a spousal open work permit, which is generally granted to the spouses of overseas students studying in Canada. This visa enables your partner to work in Canada while you study. It is a preferable choice to consider because the term of the Spouse open work permit is usually the same as the duration of the study permit.
It is crucial to note that the Canada student visa is for international students who want to study in Canada for higher education, whereas the Canada spouse visa is for the spouses of Canadian PRs and Canadian citizens who want to immigrate to Canada and become permanent residents. So, apply for a Spouse open work visa to study in Canada and bring your spouse with you.
Recently one of my friends has applied through this process and he successfully got his spousal open work permit for Canada as his wife is already studying in Canada. In the beginning he was so confused and visited a number of consultants but couldn’t find the right answer of his queries but one of his relatives referred him to visit Nationwide Visas office. I went there along with him. It was really a nice experience. Their welcoming environment and gestures were all to win our hearts. Their counselors are very experienced and have decades of experience behind them for a Canada PR Visa. They guided us thoroughly and when we got our answers correctly, we proceeded with them for further process, and it took us a few months to complete all the documentation and related procedures and once completed he got his spousal visa for Canada within a few months. Overall, it was a nice experience and their out of the box suggestions helped my friend to achieve what he was looking for.
So personally, I would recommend you to visit Nationwide Visas office or call their expert immigrations counsellors directly to get an idea of the entire process. They are one of the best immigration consultants in India. Moreover, the most amazing part of their service is their hand-holding service throughout the entire process along with the post-landing services, which is unique in itself as very few consultancies in the market provide this kind of services.
With this, I hope you will be in a better position to opt for the best possible pathways and the professional assistance required. If you really liked my answer, please hit the upvote button and share it to those in need.