As a Canadian citizen, permanent resident, or work visa holder eligible for provincial health care - if your employer doesn't pay for your provincial health care (in provinces such as BC) as well as the employer portion of a group benefit plan then you have to pay for provincial health care yourself (in provinces that charge monthly premiums). You could buy an individual health plan to supplement those provincial benefits (from a provider like Manulife, GMS, Bluecross, etc). Those kind of plans can include an allowance for prescription drugs, dental, or both - and they usually cover other benefits such as a subsidy for chiropractor, etc., eye care, etc. In Canada these kinds of plans are only available if you are enrolled on provincial health.
For visitors to Canada, 'private health insurance' means 'emergency (only) illness and accidental injury insurance'. It won't include benefits for discretionary (non-emergency) health care such as prescription medication costs for chronic illnesses or routine dental visits. That being said, visitors insurance is important, as it can help protect you from large unexpected medical expenses if a sudden illness or injury does occur. To get a quote for visitors insurance from all the Canadian companies, go to
https://www.bestquotetravelinsurance.ca/visitors-to-canada-insurance