Non-military, executive branch headcount has remained relatively consistent in
absolute numbers since the 1950s, believe it or not, at ~2 million, even though the budget has expanded enormously. Sources:
Historical table: https://www.opm.gov/policy-data-oversight/data-analysis-docu...
A concurrence in my assessment: https://www.nationalreview.com/2017/02/federal-government-gr... ("So, since 1960, federal spending, adjusted for inflation, has quintupled and federal undertakings have multiplied like dandelions, but the federal civilian workforce has expanded only negligibly, to approximately what it was when Dwight Eisenhower was elected in 1952." Note I'm not necessarily agreeing with the sentiments expressed elsewhere in that article.)
AFAIU for over half a century there's been something of a gentlemen's agreement in Congress among Democrats and Republicans that keeps the official headcount fixed while expanding government through contractors--the closest thing to a wide-spread "conspiracy" (tongue-in-cheek) I've ever seen. Of course, lobbyists and the contracting industry play a huge part in maintaining the system, but IMO that overlays the long-term political equilibrium reached in Congress.
One reason I finger Congress, and not lobbyists, as the principal supporters of the system is that Democrats would much rather have full-time federal employees, so they're clearly compromising. It's hard to say what Republicans want, but to many Republicans hiring contractors 1) squares limited government with electoral pressures to "do stuff" at the federal level, and 2) superficially provides better price signaling through competitive bidding (though if we're honest that's... complicated). Note how the numbers remain conspicuously stable across major domestic and international political shifts. It's fascinating.
State and local government workforces have ballooned, and a lot of federal expenditures are administered via state-based programs. But that doesn't conflict with the "conspiracy" noted above, it's arguably just a way for the Democrats and Republicans to jockey around it.