The oil leak should be addressed but I don’t think it’s the problem. First check the reservoir at the high pressure oil pump. This should be close to the top when the plug is removed. The fact that the truck starts cold indicates the reservoir is holding oil. The pressure regulator on the high pressure oil pump is probably the problem. You need to remove and inspect the O-ring and cut washer. If blown, replace and problem solved. I have no codes to work with so this will be a good start. If for some reason this does not fix the problem, high pressure oil pump diagnostics will be required. I’ve seen this problem many times. Good luck!