It's not a Double Taxation. STT and Capital Gain tax both are two different things. STT levied on sale and Purchase transaction, whereas Capital Gain tax is on Profit Portions only. And Rate of STT is also minor % like 0.001 to 0.1 only, which can't be comparable with income tax rate..
And In case of person who is trading in securities and offering income/loss from such trading as business income, STT paid is allowed to be deducted as business expense.
And also, GST is not leviable on sale of securities, on sale of other things like other Goods GST is applicable..