At 16 she is only a year or two away from being legally an adult. So I think you are going to need to accept that you cannot control her behaviour in the way that you used to when she was 12. Also vaping is not something you can practically control anyway; the equipment needed is small and easily hidden, so unless you are going to conduct regular rummage searches of her room it's not something you can enforce.
She probably also does not appreciate being talked down to. There is plenty of information available on vaping on-line, and while the long-term effects of vaping are still unclear, there is no doubt that it is a lot healthier than smoking. She has made a decision that she wants to do this, and I suspect that the more you try to argue about it the more she will want to assert her independence by sticking to her guns.
So my advice is to back off and pick your battles more carefully. Let the vaping pass, apart from any reasonable rules you may want to make about the smell in the house (after all, it's your house and you have to live there too). Talk about how much you care about her, but tell her that, in the final analysis, it has to be her decision.
One thing you might ask is how much it costs. Get her to work out how much of her money is going on vape every year. Is it something she might prefer to spend on something else?
Also, ask about what the problem is at school. What is making her unhappy? How else might she be able to relax? Try to support rather than correct.