Why are my distributor cap terminals burnt?

I think its way off.
However at least now you know what the timing engine is seeing.
I'm going to assume the polarity is correct.
Now you actually know what the advance looks like with two blue springs and the advance limit set the way it is.
upload_2022-2-27_17-37-50.png

I'm not sure what to suggest abou the breaking up other than I don't think its the timing. 24* at 3000 rpm I'd expect to be sluggish but not breaking up.
It could be ignition related ECU or coil or even secondary wires or cap and rotor.
It could be fuel, running low in the bowl or not getting flow through at top of transition or begining the mains circuit.