Aren’t international students who are able to buy property just very wealthy and not really there to study (hard sciences)?

Of course. Or at least their parents are. Doesn't mean there aren't sob stories in the media about students who have to break off their studies because now their parents can't afford to buy them an apartment.

few domestic students can by property either.

Just an anecdote from personal experience: the road to the main university in Vancouver runs through a large provincial park, and this road is lined with camping vehicles where students live. Some even live in Calgary (600km straight-line distance and not a cheap place to live either) and fly to mandatory lectures once or twice a week in order to make life affordable.

I don’t support the tax its discriminatory of course.

I'm not sure it is discriminatory in a negative sense. Maybe this is worth a post on its own. The point of the foreign buyers tax was to slightly cool the real estate price inflation craziness of the mid 2010s. A foreign citizen yet current resident of the region is exempt. The idea was to make speculation and offshore investment less attractive. But you can't go too far on cooling price inflation because the retirement accounts of Canadians rely on real estate inflation - either directly via owning one's own home, or indirectly as a part of a pension investment program. I would argue it doesn't go far enough, but again Canada is dependent on this and it's a liberal country built on private property.

Personally, I don't think it's discriminatory to tell a resident of Europe/Asia/wherever that they are not allowed to own a home in Canada without living there. There are people who need those homes more.