Nobody mentioned this, but do you really have time for breakfast? Your international flight departs at 08:15, which means that it will start boarding around 07:30. Changi has security at the gate, so allow 15-20 minutes for that, and you still have to go through exit channels and reach the gate first.

Maybe I'm missing something, but I don't see how the math adds up for a diversion to the Jewel, which (depending on the terminal) can be a fair walk away. I'd pick up something the night before that I could have for breakfast or else see what kiosks you pass by on the way to your gate.