What materials can be used to fill a puffy jacket?
After asking around, I had suggestions for:

Poly fill
Down
Flannel
Wool
Batting

Poly fill and down seem suitable for very puffy jackets (source), but didn't fit my vision of this particular one - might be too puffy, plus the lining would have to be more complicated to keep it distributed evenly. Flannel and wool would be warm, but they have no fluff at all, and I thought they might make the jacket feel too heavy.
That leaves batting, which has both desired properties: fluffy, and can be easily quilted to only the lining.
The particular material I got was Soft n Crafty 80/20 batting, which is advertised as: low-loft, with a soft drape, and specifically mentions garments as an application! It's just a little puffy, and not as heavy as wool.
I originally came across this in a store, so it was sheer luck to find exactly what I was looking for. Now that I know what it is, the key words appear to be &quot;low loft&quot; or even &quot;ultra low loft&quot; - searching on this gives me more product results, as well as some posts about sewing with it.