Why wouldn't other countries try to influence the course of the world government?
You don't need the President if you have Senators and Congresspersons that have mastered the art of not passing any bills and falling asleep on CSPAN.
Influencing a presidential pick rarely pays off unless they are a "disruptor" who promises to restructure the civil service and diplomatic offices. Those are the groups that foreign nations deal with. They want influence over those because they are the intermediaries that can change a President's mind on an issue.
https://www.defenseone.com/ideas/2024/01/foreign-interferenc...
https://apps.dtic.mil/sti/trecms/pdf/AD1213704.pdf looks to be an excellent review of the subject, though I've only now discovered it and therefore haven't read it in detail yet.
E.g. "Russia has been trying to influence elections worldwide since the 17th century (Shimer, 2020). Election interference is also a goal of many Russian military operations. Many of these disinformation campaigns aim to sow discord among the population and attempt to get elected the candidate that best suits Russia’s interests."
It seems quite clear to me that every nation participates in misinformation campaigns to affect other nations' elections in was beneficial to the actor.