I would guess Shen a little of both in terms of Bloomery vs Crucible. The Documentary Stated that Crucible was known in the middle east particularly Iran, and that's on the Silk road If The Norse could get that technology form there then it's entirely possible it either came from China or Went to China.
Well, the Damascus type crucible steel talked about in the Viking sword video is actually different from the blast furnace steel made in the traditional Chinese way.
Crucible steel starts with very low carbon content wrought iron probably made with the bloomery method, then add a carbon source such as ash and a flux such as glass, sealed in an airtight crucible and heated to a very high temperature until everything melt and mingle. When cooled, the slag bond to the flux and you are left with a very pure high carbon steel ingot.
Traditional Chinese blast furnace way of steel making doesn't go through the bloomery stage. The iron ore is heated directly to very high temperature until it become liquid, since the iron is not sealed in an airtight container it absorbs a lot of carbon from the fuel source, so liquid iron is very high carbon content pig iron which pooled and formed into ingot. To get wrought iron, the liquid pig iron is stirred in open air to burn off the carbon. Finally to get steel, high carbon steel pig iron and mixed with wrought iron to form intermediate carbon content steel. The final steel made in the Chinese method was probably not as pure as the crucible steel, but the benefit is that it can be cheaply made on large industrial scale.
I don't know if it is possible to tell Chinese blast furnace steel apart from bloomery steel on a microscopic level, and may be that's why I can't find any information which type of steel ancient Chinese swords were made from.