I agree with you in principle, but I'm not sure how feasible this given that I literally can't think of how to implement it. Political advocacy groups use complex hierarchies of shell companies and revolving payments to get money from super-donors into advertising. FB can't just release an invoice saying something like (Payment: 106,000; Sender: Robert Mercer) or "paid for by the Russian Federation". It would say things like "paid for by the Committee to Improve America", which receives money from the Pro-Families Committee, funded by the Traditionalists Group, an advocacy arm of the Peers Think Tank, which has ~100s of wealthy donors.
Then we require that all money spent on politics (AND related political influencing, like money to Jud Watch and Cit U and Cato and AEI and Bradley Fdn and Am First and Koch Found and Americans for "Prosp" and the NRA) requires public disclosure of who's behind it.
We already do much of this for direct campaign donations and in real estate. It's just a matter of political will. And one side has spent 4 decades and hundreds of billions on creating this money-first system, so they are very invested in not changing it. If you care, the first thing to do is get Congress to pass a law rescinding most of Cit U decision.