I presume this is an apocalyptic setting after catastrophic effects of global warming have completely melted the polar ice caps and flooded major continents???
Don't answer, don't want you to divulge any spoilers.
What would I have aboard the situation you describe.
First of all, if he is going to making long voyages, he is going to need lots of space and capacity to carry wood. A steamer the size you describe will burn a cube four foot square at about 2000 pounds of firewood per long steaming day. In this case I would tow a small dinghy or raft for extra wood and as a survival tool.
Navigation tools, two compasses, one for backup, sextant, charts if available. GPS unit.
A good Galvanized bucket: For carrying out ashes, dipping water from over the side to wash down the decks, bail water out of the bilge when the bilge pump doesn't work.
A Bucksaw/bowsaw/pruning saw for cutting firewood.
Primitive firestarting materials along with several disposable lighters and waterproof matches.
An axe for splitting wood and as a weapon. A good hunting style knife for just about everything.
A flintlock shortbarrel musket. Can be used as a rifle for large game, a shotgun for small game and can be used for fighting and signaling as well. Gunpowder (blackpowder) can be stored in large quantities or made from a few different ingredients and flintRocks are simply found in most places of the earth. Projectile can be anything, nuts and bolts, rocks etc.
Handtools, wrenches, a vise etc.
An assortment of pipe fittings and pipe which are the same of which makes up the boats plumbing, spare packing, gasket material.
Oil to lubricate the engine.
Candles, kerosene lamp and kerosene.
A good comfortable cot with bedding.
Dried meats like fish and beef jerky. Grains like wheat and dried corn, oats. MRE's and other basic survival supplies, canned goods if possible. Iodine tablets for purifying water/steam condensing coil also for making potable water. Medical supplies, aspirin, bandages etc. Tea, If possible, antibiotics, painkillers, anti- inflammatory drugs. Cooking and eating utensils. A small woodfired survival stove. Containers of freshwater. Fishing equipment. Soap for hygiene and general cleaning disinfecting. extra clothes, a few hat types to block the sun. Tarpaulin for shelter during rains or intense sunlight.
Mutli-band survival radio with built in handcrank dynamo for power. The engine would also have a small generator to make electricity. Maybe some solar panels on a cabin roof. 12 volt lights, portable 12 volt pumps. Flashlight/torch.
A spare propeller, maybe a spare prop-shaft
Strong insect repellent.
lifejackets, fire extinguisher.
A good literary work that can be read multiple times and still maintain interest.
What else??
-Ron