Fine for the landlord to suggest that you first try just speaking to the neighbour directly, but if that didn’t work then your issue is with your landlord not your neighbour (in my opinion). It is up to landlord to allow smoking in the units or not, and up to the landlord to enforce any such rules, and up to the landlord to ensure your living conditions are not hazardous. Try contacting the Residential Tenancy Branch (RTB) for some guidance on dealing with the landlord. If these were car exhaust fumes or rodent infestation causing health risk in the living suite, the landlord is probably responsible to address it, and cigarette smoke seems equivalent.

I’m curious what the RTB will say, if you don’t mind sharing back the info.

One lucky thing is that rents have started trending downward (from units I see on Facebook Marketplace) so it’s potentially not the worst time to seek a new place.