IANAH (-istorian) but from my layperson reading, the technology level of forging drove all of metallurgy. I am a metalworker, so the part I know is that everything is about getting the forge hotter and hotter to work and treat tougher and tougher material. Copper can be cold worked or annealed in a wood campfire. Coal will get you hot enough to work brass and bronze. Copper and its alloys can only be cold-worked to a point though before they will work-harden and crack, so you need the heat.
By the time you get to iron and steel, you need coal, coke, sophisticated flue designs, and mechanical bellows to get the heat needed to hot-work it. You won’t get anywhere trying to cold work iron. Even if you had a modern steel hammer, at best you’d crack the piece. Iron is fairly brittle, and cast iron is very brittle.
It takes exponentially more technology to get to each next level of forge temperature, so it took quite a while to figure out flues, mechanical air management, etc. Coke especially was a real breakthrough cue the dad jokes and gifs about cola
