The tiles themselves work fine, but how to best mount them? where do you need them? Can you make them thinner? do you need anything underneath? what kind of gap do you need between tiles? Those are the things they're hoping to understand in these tests.
The Shuttle tiles were technically reusable AFAIK. The issue was that they were very fragile and the Shuttle for the most part could not tolerate any heat getting through the tiles (being aluminum), so every flight needed to have a perfect heat shield. Starship is a bit better on that end, as stainless steel is a lot more capable of tolerating heat and I think the tiles are a bit less fragile. Still, would be ideal to figure out how to not drop any tiles.
Which is a little easier to do when your craft is shaped like a plane and not a simple cylinder. The loading and positioning were easier to model and then achieve in flight.
The shuttle also flew with repair kits and glue that could be used in a vacuum. The astronauts could perform an EVA and work to replace damaged tiles and there were published plans on how to do so. NASA unfortunately figured out very late that using the Canadarm to image the bottom of the shuttle immediately on achieving orbit was extremely necessary given the icing problems of the external tank.
I don't quite understand how the airplane shape made it easier to model the loading and positioning? (Not saying you're wrong, just doesn't fit my intuition and I'm curious).
My understanding is that Shuttle didn't have to answer the questions about tile gaps etc because it used glue rather than mechanical attachments, if that's what you mean by positioning.
You can approximate space shuttle reentry to roughly a 2d surface entering atmosphere. Because of airplane shape, the tile side faces atmosphere and the plasma goes around plane edges. Where as starship being cylinder doesn't have any separation boundary and plasma roughly goes more than 180% of the cylinder.