Hi Crash_144,
Welcome to the forum. The schematics for these controlboards are impossible to find... I've tried for years

So, we will never find a diagram with the exact value of the burnt resistor on your your pcb.
But, there is still hope...
Do you have an ohm-meter? I hope you have, because with a little luck, the resistor may still have its original ohm-value.
But be careful not to bend it or otherwise expose it to any physical stress while measuring, as it is likely VERY fragile in the present state.
Other components connected to the resistor are most likely faulty as well, since a resistor only gets that hot when something is very bad. Hmm, you said that everything works except auger motor... that's good news. Try to trace the augerterminals on the pcb backwards... that might lead to the resistor and surrounding components. On my Quest Plus stove the two blowers are controlled by the triacs with heatsinks and the auger motor is also controlled by a triac, but this has no heatsink. I count three components on your photo that look like triacs.
Check for correct function of the auger motor by applying 120 volts directly to it with some test cables. If, say, the windings on the auger motor are fried, this could have led to the fall of both the triac and the resistor.
Take care when working with naked grid voltage!! If you haven't tried this before, please let an experienced person do it.
Also check the wiring for any short circuits.
Good luck and keep us posted
Bo