The damage to the MOSFET looks typical of over-temperature. The damage to the gate diver is collateral I would say.
From your picture the heat-sinking looks inadequate.
Also the PSMN3R9 NMOSFET has an insulated case while the IRF3205 case is not insulated. It is not clear to me which NMOSFETs you are actually using, but if the meatsinks on the printed circuit board are not floating, the IRF3205 will cause a problem.
A 68 Ohm gate resistor sounds high for this application, around 10 Ohms would be expected.
Also, I am not sure that the gate driver is up to the job, but I have not analyzed the circuit in detail.
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