Interesting, I thought all appeals to the USSC required moving through the federal court system first.

It's uncommon, but the Supreme Court also has original jurisdiction, "In all cases affecting ambassadors, other public ministers and consuls, and those in which a state shall be party." U.S. Const. Art. III. Here, Texas attempted to sue four other states over how they conducted their elections, so it fell under original jurisdiction.

This was original jurisdiction. Cases between states start here.

The supreme court in fact ruled against Texas in dismissing the suit, by mkaing it clear that each state has sole discretion on how to run their own elections, as prescribed by the Constitution. Whether state elections laws were followed was for state courts to decide, not Texas and not the federal supreme court

States can run their own elections. So long as they abide by Article2, which indisputably, PA, MI, WI, GA did not. NV did use their legislature to make the changes which is why they weren’t a defendant. Texas’s position was that they states didn’t follow the constitution and the winner of these federal elections would effect rule and law in Texas.