Use PNG when editability and compatibility matter
PNG is still the safest option for design handoff, simple transparency workflows and environments where maximum compatibility matters more than file size savings.
Use WEBP when website delivery matters
WEBP is usually the stronger choice for modern websites because it helps reduce page weight while keeping visual quality acceptable for most product, marketing and content flows.
Operational rule of thumb
Keep a safe master format internally, then convert outward for delivery. That is one of the clearest reasons to run an image conversion pipeline instead of managing every output by hand.