Running Jacket - Lightweight & Breathable NOT waterproof?

Been doing some research on this all winter. I don't live anywhere where water/rain is a worry.

Ideally it'd be a super lightweight jacket i can layer over a longsleeve layer for particularly cold days but is still breathable and isn't moisture retaining (or as minimal as possible).

I've currently got the Houdini and the R1 Air. The houdini is insanely sweaty and practically useless for running. The R1 Air is very cozy but it's kind of heavy and I start to overheat after 15-30 min of running.

Is there anything in between? Ruling out any need for waterproofing I've been looking at maybe the Brooks Canopy or the Path Projects PX Shell but I'm having a hard time finding something that's lightweight/breathable that decidedly isn't also trying to be a windbreaker/water shield. Would love any advice here.