There is no lower court that may hear a case of State vs State.
I think the Supremes decided this really wasn't a state vs. state case. This was an outside state noting that what happened within another state was unconstitutional.
Personally I believe every citizen of the US should have standing to bring a case against every state that ran its elections unconstitutionally, but unfortunately it appears that you only have standing if someone has caused you to lose money. Truly sad.