ST is levied on the same of goods irrespective of the buyer. You're not exempt just because you owe other forms of tax to another government too. If a seller chose not to charge you on that basis, it would come out of their pocket.

I see it as a bad tax personally. It affects lower earners proportionally more of their wealth, and is often politicised (as when they levy higher tax on sugary soda or smokes). I don't necessarily hate the idea of discouraging smoking, but the same legal argument can then be used to tax things I might see as normal. That's how legal precedent works, it generalises and tends to be applied in unexpected ways.