That clause seems to be about how the Court can go about deciding cases under it appellate jurisdiction.
That said, I wish Congress would assert its authority by declining to pay the bills of the Supreme Court. Try holding court with no electricity, no heat/AC, no clerks, and no paper, computers, pens, pencils, etc. The Supreme Court is the only federal court whose existence is due to Constitution, but Congress has budgetary authority, and I wish Congress would assert its authority, just once, when a subordinate or co-equal branch tells Congress to jump in a lake. Just once.
Civics lessons say that one of the checks and balances between the three co-equal branches is that Congress holds the purse strings. Okay, Congress, to quote Khan Noonien Singh, "explain it to them." That would be fun to watch.
Congress just rolls over and takes whatever abuse others decide to dish out yet still pays their bills. What good is the check if it is never used and opponents flaunt it.