I'm sure Starship will be better, but 40 times cheaper? I doubt it.
https://www.spacex.com/media/Capabilities&Services.pdf
The biggest cost is throwing away hardware. If you're not doing that, you can amortize your entire hardware cost over the number of launches. At Falcon's launch cadence that's still going to be significant. But Starship is designed to do hundreds of launches per year, and if they manage it then hardware cost per launch is almost nothing. Then you're mainly paying for fuel and ground services, which are about a million dollars each. 100 tonnes to LEO for $2M gives just $20/kg, leaving plenty of margin for SpaceX at $50.
It might seem hard to envision putting that much cargo into space every year, but if we did solar power satellites at scale, that's exactly what we'd need.
No, $97M is for a launch with reused boosters. 63,800 kg to LEO is when the boosters are dispended.
The payload is definitely for expended boosters (check the footnotes). I agree it's not very clear about the price. Wikipedia could be out of date I guess and they're not giving a discount for booster reuse? But then why would anyone ask for reuse?
Advertised price on Falcon Heavy is already just $600/kg to LEO. A big part of that is the throwaway upper stage, which Starship eliminates.