It sounds as though you are offering me the fallacy of false choice. (Which of three branches when the choice is not limited to just them, or just one of them.)
It is the responsibility of all Americans to insure compliance with our laws. It OUGHT to have started with the Democrat party vetting his credentials, but as they are basically anti-American lunatics who will comply with no inconvenient law if they can get away with it, it is safe to say that that particular check on law breaking isn’t any sort of impediment to lawlessness at all.
The next check SHOULD have been the Agents of each state tasked with confining eligibility for elections. The State election bureaucrats. They should have KNOWN what the requirements were, and they should have INSISTED on proof that he met them. They did not.
The NEXT check should have been the Electoral college who ALSO should have KNOWN what the requirements were, and insisted on Proof that he met them.
The NEXT check should have been both the Congress and the Courts. Again, they should have KNOWN what the requirements were and they should have REQUIRED proof that he met them.
Finally, it is the consent of the Governed. The larger body of American people who by passivity concede his authority and legitimacy over them or by opposing challenge it.
Let us not even speak of the role of the 4rth estate who were in fact collaborators with the usurpation of legitimate governance. But THEY should have sounded the alarm among the people at a time well before the Democrat Primaries.
Now we must go through the hard slog of attempts through a thoroughly frightened court, and efforts to inform public opinion without the Megaphone of the Media and Entertainment industries.
No argument as to their responsibility. The only thing in question is their competence.