How to make century eggs?
What I think you have made is brined or salted eggs which are very different from the blackened "century" eggs.

Salt preserved eggs do need cooking, at least the egg white will need heat to solidify. If you extract an egg yolk and cure that with salt and sugar (no added water), you can use it almost like cheese, the texture would allow you to grate it over pasta without cooking for example.

The blackened century eggs do not require cooking, because it is already cooked, or the proteins fully denatured. It takes alkalines and salt to achieve that. The high pH usually comes from a combination of lime (calcium oxide) and calcium hydroxide. The process is very different. Strangely, you get the opposite of brining when it comes to textures - solid "white" and runny yolk vs runny white and somewhat hardened yolk.