TYRES are not covered. They are a wear item like brake pads or clutches in a car. The WHEEL is a metal part not subject to wear. If its failed then thats because of manufacturing or design issues and so it IS covered under warrantee. Unless its an all in one tyre/wheel as is sometimmes fitted to small shopping centre type devices. In which case it may NOT be a warranty part. Bit even then, theres a huge difference between unexpected failure, and normal wear through use, or abuse.
So its important to understand why/what failed. But at 6 weeks, I would throw it back to the manufacturer.
But that tyre looks OLD and dried out and so has failed due to rubber deteriorating over time. And that metalwork looks old rusty and tired too. So hardly 3 weeks old.