But insurrection is a crime against the United States Federal Government and the commission of such a crime would obviously be covered by federal courts.

Sure - but again, it's not at all uncommon for state courts to have mirror provisions or incorporate by reference provisions of federal law, and to have violations of federal law have an effect under state law.

Trivially, there are lots of instances where being convicted of a felony will affect your ability to do something under purely state law. For example, if you commit a federal felony (say, insurrection against the federal government) you might not qualify for a state license (say, get a state liquor license). If the state rule doesn't require a federal proceeding but simply incorporates or mirrors some federal requirement, then a state court has jurisdiction to make a finding about whether that federal requirement has been met.