I have a Chinese passport with a USA H1B visa, originally scheduled for a flight from NKG (Nanjing) to SFO via ICN on the same day. Asiana Airlines rescheduled my first leg exactly 24 hours earlier so I will have an entire day before my second leg. I don't mind staying in Korea for one night to do some light sightseeing, but do I qualify for the 30-day visa exemption rule?
The KETA has nothing to do with the 30-day exemption. It's the Korean equivalent of the ESTA and brethren, an authorization to fly to the country that issues it, for people who have visa-free access. You do not have visa-free access, hence you are not eligible to a KETA. But as I said, it's nothing to do with the visa exemption scheme.
That scheme is for non visa-exempt nationals who are in transit through South Korea. Like you. Your flights match the conditions. And you need to hold a physical visa or a residence permit issued by (in your case) the US. So supposing your H1B is a physical visa in your passport, you are good to go. Enjoy Seoul, albeit briefly.
You should be eligible for the 30-day visa exemption since your flights match the transit conditions and you have a valid US H1B visa in your passport.
I'd say go ahead and enjoy that day in Seoul - even just a brief overnight stay could allow you to see a few top sights. It may help to book a local guide. That way you can hit some top spots efficiently with an expert. A guide could take you to major attractions like Gyeongbokgung Palace and Insa-dong, plus recommend somewhere good for a meal.
Found this one that offers private tours in Seoul https://gowithguide.com/korea/seoul/guides Might be a good way to make the most of your short time!
Have fun exploring and safe travels!