It wasn't a real good slathering, and mistakes were made where the Supreme Court ended up as its own judge.
The very same Founders did something very suspicious when they wrote up the rules for the Indiana Territory ~ the state Senate was turned into the chief court ~ boom boom ~ boom boom ~ boom boom ~ tympanic noise resounds in the hall.
Same guys; a dramatically different idea for a Senate. BTW, the Indiana legislature was still handling divorces in acts of the legislature in the late 1800s! That was after the reform of taking it out of the hands of the Senate alone.
The other territories and states that were laid out to rule the Old Northwest as it was carved up into states did pretty much the same thing ~ use the senate as a court ~
I think if we needed anything to give us a proper perspective on the Senate, it would be as a court with jurisdiction on all cases at law arising out of federal law. That would include any possible conflicts with state laws created by federal law.
Our form of government is unique and reflects what the States were doing at the time, more than the Brit system.
The Federal Senate was modeled on the existing Maryland Senate and retained State representation, in modified form from the Articles of Confederation.
Congress has plenty of power over courts. It doesn’t use them because the ruling class generally likes the results.