Marmot fleece jacket most of the time when chilled, lightweight (no lining/insulation) Outdoor Research rain jacket with hood for rain and/or wind. Combine both with a merino long sleeved base layer on colder days.
I did the CF in Sep/Oct 2021 and it was close to Zero C several mornings on the meseta starting in Burgos in early October. I layered both on those mornings, but typically was able to shed one layer after the first couple of hours as temperatures rose. I also wore the fleece on cooler evenings - more than anything else, my arms get chilled!
My L.L. Bean 850 weight down puffy is very light weight, warm, and compresses into a built-in stuff sack, but is not waterproof. Also the shell is easily snagged/torn, so it stayed home during my caminos.
If I were expecting colder temperatures, I would invest in a waterproof jacket/parka with some insulation and probably still bring a fleece to use as either a mid-layer or outer layer on milder days.