It was more of an invention of the French philosopher Montesquieu in the 1740s, The framers of the constitution were imbued in the theories of those French philosophers (and Locke, and other English philosophers) so at least some of them must have had the idea of the three branches in mind by 1787
Or as if they were amateurs who didn’t know what they were doing. If a constitution is to have any meaning at all, then someone must have the power of judicial review, and the Founders neglected to say who that might be.
But the Constitution does contain one Article each for setting up the legislature, the executive, and the judiciary. That sure looks to me like they’re at least comparable in status.
I see from your profile that you are from England. That very likely is the cause of the confusion here.
My understanding is that in England, the word “government” refers strictly to the elected politicians in the House of Commons, in other words, the party in power. In the US we use the term “administration” for the same basic concept.
In the US, we use the term “government” for the entire apparatus through which the functioning of governing is carried out.
In other words, anyone paid by the government is considered to be part of the government. This includes people like clerks, janitors, scientists at national labs, and zillions of other people. And judges.
In a parliamentary system, the prime minister, cabinet and elected representatives of the prime minister’s party or coalition are indeed referred to as the government.
And that’s the other side of the problem. Such long-term appointments make it very hard to deal with a person who is a problem. We can allow someone to be re-appointed if that’s what people want, but terms should be much more limited. Maybe 10 years, isn’t that what the FBI director is limited to? Long enough to bridge multiple election cycles, but not long enough to screw things up for 30 or 40 years, like we’re looking at now with the current SCOTUS crop.