Do I need a neutral wire for a smart dimmer?

It depends on the model. Lutron Caseta dimmers (both the original PD-6WCL and the Diva DVRF) are widely cited as no-neutral-required, which is why they dominate retrofits in older homes. Most Wi-Fi dimmers from Kasa, Tapo, and the standard Leviton Decora Smart line require a neutral. Check your box before buying.