You're along the right lines, but it's gnarlier than that. National politicians are more like WWE wrestlers or reality show contestants. They have some freedom of action, but not much, and they must stay within the lines of the script. Tellingly, none of them actually legislate anymore, with the exception of the occasional bit of grandstanding that isn't intended to ever get past being a bill. All the bills that do become laws are written by private lawyers working for known or unknown principals, who then hand them off to lobbyists, who then arrange for a politician to sign off on it.
We receive some clues as to who the real shot callers are, because certain agenda items reliably receive bipartisan support. So for example we can conclude that whoever really runs the USA is fully in favor of involvement in the Ukraine war. There's enough publicly available information to build a relatively complete profile of the rulers, but not, so far as I know, enough information to reliably identify any specific persons. Needless to say, efforts to publicly develop and share that profile are rigorously suppressed.