Everything that comes out of a petrochemical plant can be made without oil, in fact BASF had recipes in place for decades now and is switching sources as the price shifts. Push come to shove they can produce everything from starch. It’s also why they hardly blinked when Russia turned off the gas.

The carbon that actually ends up in steel is a quite negligible amount (usually under 1%, over 2% you get cast iron), you can get that out of the local forest, and to reduce the iron hydrogen works perfectly, the first furnances are already online.