When democrats lose elections, they somehow get to keep their people in place and run the country from their administrative perches.

That's not our system.

Yes, it is. The federal government operates under a Civil Service Act, where most federal employees are supposed to be hired and retained based on merit and not based on whoever won the last election:

en.wikipedia.org - Pendleton Civil Service Reform Act

There are about 4,000 upper level management positions that are Presidential appointments (about a third of which require Senate approval). The rest are almost entirely protected by the Civil Service Act from being fired or replaced simply based on their political views or whether they support Democrats or Republicans (or MAGA or woke).

Again, we live in a country where Congress writes the laws and generally gets to decide what the government will do and how it will do it. And the law is that most federal positions are to be filled and retained by basis of merit, not affiliation with who one the last election in either party or policy.