Advice for scaling poison damage

Hi there I made a build that uses cospri's to poison along with bladeflurry. I was under the impression that physical damage applies the poison (cospri's) and then the DoT is scaled off the hit from that physical attack?

I am also wondering if chaos damage is worth taking in a skill tree, chaos damage from my understanding would apply to the DoT effect of poison?

take those phys/chaos passives near Shadow start. Other than that, scaling only the DoT usually not worth it (maybe the poison cluster).

Area damage would be best but there are not many sources. jewels with generic increased damage and AoE damage would be decent for that

edit: I also forgot about chill and temp chains that both affect the poison duration thus indirectly increase the damage. And ofc Vulnerability curse