(using Vancouver as an example, after the foreign buyer tax the city still has an incredibly low near 0% rental vacancy, which makes secondary home investment enormously profitable and continues to keep prices lofty)
This doesn't mean that it wasn't a good idea to address the foreign buyer problem, but it was clear that the system instantly shifted to compensate for the lack of foreign buyers, and new buyers appeared. There was plenty of local buyers, many of which had existing properties with inflated land values they could borrow against and the ultra low interest rates from the pandemic that aided them in bidding up properties to buy. Good for local buyers to have less foreign competition, no real change for local renters.
The most real direct outcome of the foreign buyer tax was the nature of the housing product that was made changed. Previously there were companies that were building "luxury" condos explicitly marketed as pied a terres to a foreign audience (largely from major cities in asia). Overnight this sort of thing went away and the same companies that were previously pushing these products instantly pivoted into building purpose built rental buildings for locals.
Ultimately I think the foreign buyer tax is good for local renters, but further work needs to be done.
It's not unusual for someone to use their HELOC to buy and 2nd or 3rd property and rent it out.
Of course with rising interest rates (and mostly variable mortgages) that's all coming home to roost now, al la USA in 2008.
The fact that there was significant amounts of foreign buying is not in contention. You can google Globe and Mail articles from ~2016 that cite these figures.
One of the biggest examples would be in real estate, where foreigners could be comparatively very wealthy compared to locals, and can thus out compete locals and dramatically raise the price of real estate.
This is why some jurisdictions that found that the amount of properties being purchased by foreigners was becoming startling have brought in foreign buyer taxes to try to even out the distortions in the economy and make it more fair for those who earn their incomes in the local economy.