Do engineers manufacture things?

I am just wondering wether engineers, such as electrical or computer engineers actually also manufacture things physically (as in assebmling products for example). If not, who does that and what exactly do engineers do? Also another question, could such an engineer as mentioned before manufacture and design a device or some product by himself. In case they don’t usually do it, as per the other question, I was thinking maybe they could use something such as a 3D printer, as it makes manufacturing a lot easier as far as I know. Would a 3D printer be precise enough for things such as CPU though for example, or other similar fine objects?

Thanks