Stick drift appearing after 8 months on a brand new controller is pretty textbook defective hardware, and you're right within the window. Sony's standard limited warranty runs for a full year from purchase, so you've got roughly 4 months of coverage still sitting there if your receipt shows the purchase date.
Your best move is to reach out to PlayStation Support through their website or phone line with your receipt handy. Have photos of the drifting in action if you can - showing them a video of the stick acting up on your phone helps. They'll likely ask you to try calibrating the controller first (it's in the settings), but given the pattern you're describing, they should authorize a replacement or repair without much pushback. Keep your receipt and original packaging if you still have them, though most support staff won't require you to ship the controller back in pristine condition.
One thing worth knowing: if Sony declines for any reason, check whether your credit card or any purchase protection plan covers defective items - some do, some don't. But honestly, at 8 months with a known manufacturing issue, you shouldn't need to go that route.