Toyota's sports cars actually show pretty well at how adverse they are to making them.
The Supra has a BMW engine, a BMW gearbox and a BMW interior with a BMW infotainment system, while the Toyota 86 is a joint project between Toyota and Subaru, with a Subaru engine and built in Subaru's plant.
They’re definitely Toyota cars but not really sports cars. They’re just hot versions of the Corolla and Yaris, which are definitely not sports cars. Unless we also define the Tesla Model S Plaid, BMW M3 and the Mercedes-Benz E63 AMG as sports cars.
The Yaris GR is not a hot version of the Yaris. It's designed as a homologation special with a new chasis (there's no regular 3 door Yaris) and engine. Calling it a hot yaris is a bit like calling the Renault 5 Turbo a hot Renault 5.
The Corolla is closer to a hot Corolla as it uses the same chasis.