What is that noise actually? It's clearly not JPEG artifacts. Is it dithering from converting from a higher bitdepth source? There do appear to be very subtle gradients.
That said, the actual size of this image is massive compared to where it needs to be, and looking at it, should definitely be able to quantize down to 32-64 colors and reduce the size to even 4x the render size... let alone just using svg, as others have mentioned.