Short answer: for marketplace sales, yes — section 24(ix) of the CGST Act makes registration compulsory for anyone supplying through an e-commerce operator that collects TCS, whatever the turnover.
For sales on your own website only, the normal threshold applies (₹40 lakh for goods in Tamil Nadu), because you are not supplying through an e-commerce operator.
There is a relief notification for intra-state marketplace sellers below the threshold, subject to conditions — check whether your marketplace supports it before relying on it. Since you sell on a marketplace today, the simplest safe course is to register.