Refueling won't be possible until tasks can be interrupted and resumed. In the case of the modded functionality of forging you can easily do that: just require a sufficient amount of fuel as part of the process. You can easily assume feeding fuel to the fire at appropriate moments is just a regular part of the process: there is no need to micro manage it as it just adds tedium. The fuel requirement is still valid though, but just bake it into the process.
A case where you might want to actually handle refueling is the smoking of meat/fish, but you don't want to be tied to your homestead for the rather lengthy process (yes, you can check nearby traps, but hardly perform any quests).