You're right that there are many issues, or I would call them regulatory areas, to cover. Whether they should be covered in one piece of legislation or in several I leave to you, but I certainly agree that the big tech giants play on a number of consequences regulated under many laws. You have identified privacy and elections, and I think also perhaps monopolies: are they a utility offering a public service as opposed to a company that gathers information to give a service and in the meantime makes certain profits? That's another question.
All of these questions are relevant. They are all relevant, they all need to be addressed. I'm not sure mechanically how it works, but I think generally they should all be looked at. The regulators should be able to talk to one another, because these issues intersect.