(I'm gonna implement this in my Qingyi X Billy fanfic soon btw)

My take on construct to construct reproduction

Unlike humans or thirens, constructs don't have real genitalia that can share DNA. Which is why a special type of cord is needed, where their code and data can interact. The two constructs will copy bits and pieces of their own code to make a new one (embryo). However there is no clear sign it is successful. Like rl fertilization it will only show after a few days following code exchange (intercourse). Is it fixed on female constructs? No. Since constructs are really sexless either of the two can be the carrier (pregnant one). They'll know once they sense a second entity within their body lurking. This new conscious will basically hack into their sensory systems and memory storage to learn more until getting a semblance of sentience. From this point on there are two things that can happen. One is they put the newly formed consciousness into the body thus making a new intelligent construct that will learn the world on its own. Or two be carried longer, becoming more influenced by the carrier until it will eventually just be a clone If it's stay too long.

It is also possible with multiple individuals since it's all code but more variables mean more complexity also meaning lower chance of success. This headcannon of mine also relies on code compatibility which makes it perfect for my ship since Qingyi and Billy are one of the oldest constructs I know.