This is very interesting. Zambian and Nigerian English also use "to take" like this. Because it was in this lesson, I would have thought that use came from the local language, but based on dsimonds info, it sounds like not. Perhaps it is old British English that was incorporated in its colonies.
I agree with @Anna662726. I might take sugar in my coffee but I wouldn't take coffee.
We could take hard drugs or take our medicine, but we just drink (or have) coffee.
If you wanted to be humorously old-fashioned or literary you might use the word partake:
"I had indeed partaken of this beverage over the years."