“State judges CANNOT hear or rule on cases that fall under the exclusivity of federal jurisdiction.”
You are correct as to exclusively Federal issues. However, the vast majority of issues addressed by SCOTUS aren’t exclusively Federal. The only truly exclusive issues for Federal jurisdiction are suits between states, bankruptcy, patent/trademark/copyright, admiralty, antitrust, and a few others. Think about how many cases have arisen over the years at SCOTUS that are outside those areas; it is most. The vast majority of Federal issues arise not when it is exclusively Federal jurisdiction but rather concurrent jurisdiction in which a Federal question predominates (or diversity jurisdiction).
State courts are courts of general jurisdiction and thus given power to hear almost any case arising under either Federal or state law, except those of exclusive federal jurisdiction (which, again, is not most issues that come up). Most cases implicate both state and Federal issues and, where not directly on an issue of exclusive jurisdiction can be heard by state courts.
That doesn’t mean a defendant might not try to remove it to Federal court on either Federal question or diversity of citizenship grounds, but there is no bar on state courts hearing it where it’s an issue of non-exclusive jurisdiction which, again, is most cases.
And so, state court judges do still often run into interpretation of Federal issues, including matters of constitutional rights, which is directly relevant to serving on SCOTUS.
For over 30 years as a litigation analyst in the insurance industry I dealt with a great many very high profile cases in both state and federal court. Generally speaking, state court judges were pretty piss poor, and the vast majority were politicians first; and we ALWAYS tried to get the case removed to federal court, if the controversy warranted it, as the caliber of judges in federal court was far superior.