The Wood First Act in British Columbia was really meant, I think in the words of the government of the time, to “create a culture of wood” and wood construction in government infrastructure buildings in British Columbia. It hasn't forced the government to build with wood, but that bill, like this one and the Charte du bois or the wood charter in Quebec, was designed to put a spotlight, as you say, on wood as a great construction material for modern buildings, especially with mass timber construction.
Since the Wood First Act in British Columbia was introduced, there have been many provincial infrastructure builds, including the airport in Smithers. A fire hall on Vancouver Island was built out of engineered wood. That's what the Wood First Act in British Columbia was meant to do—to complement that across the country with federal infrastructure.