Is this even possible?
Let’s say for example congress decides it wants to set term limits for judges on the Supreme Court. The bill gets passed and signed into law.
Then some advocacy group challenges that law all the way up to… What? They couldn’t take this all the way to the Supreme Court could they?
Since the term of Supreme Court Justices is set by the Constitution*, it would require an Amendment to the Constitution to change it. If Congress just passed a law saying it, it would have no legal standing.
Yes, but the law wold have no standing because it was unconstitutional. The OP asked who makes that determination. And even if there is a lower court to decide originally, where does the appeal go?
There is no reason why the Supreme Court couldn’t decide this. They are the final arbiters of the Constitution. There is also no real recusal policy and no actual oversight about recusals so there would be no issues there (see some of the times that Clarence Thomas has refused to recuse himself in the past on decisions related to laws that his wife had lobbied and campaigned heavily against.)
In this case, the law is so clearly unconstitutional that it would be struck down at the district level. If that were for some reason appealed, on of the circuit Court of Appeals would uphold that decision. I doubt SCOTUS would even bother granted cert to that decision of the Court of Appeals since there would be no controversy about the decision, but they would certainly be free to take it up and decide it, as is their Constitutional prerogative to do.