What the level of repair/maintenance needed if you only operate two to three weeks at a time? Is the ability to conduct basic repair like replacing a component here there sufficient? Is the ability to overhaul of an engine needed?
Where did you get 2-3 weeks from? Even the 056 can stay out at sea longer without replenishment.
Basic repairs and overhaul should cover pretty much everything except major structural work. With engines overhaul, repair and replacement being a core fundamental requirement.
All it would take is a coin sized FOD to be missed and sucked into an engine to make that engine unsafe to use without overhaul and repair. That’s a fighter out of action if you can’t replace the engine.
Space on a carrier is finite, and so will be the spare engines carried. So being able to perform basic repairs of damaged engines would massively ease your logistics burden. Similarly, being able to overhaul engines will multiply the number of sorties your fighters can perform during a deployment.
Bird strikes, heavy landings, accidents etc can and do all happen, not to mention basic wear and tear from heavy deployments. So being able to repair any such damage and replace worn parts is a non-negotiable requirement for a carrier.
And all of that is just your normal peacetime needs. These are warships, so need to be designed for war. During war, you have additional hazzards like bullets and missiles being shot at your planes, so being able to repair as much of that damage as possible is also critically important. During the falklands, harriers were being sent back up with patched up bullet holes sometimes only hours after returing with those holes originally.
To allow them to do this, all carriers should have a big spares inventory including everything from nuts and bolts to fresh engines, with all the tools and equipment needed to pull out broken/damaged originals and replace them with spares.
Carriers also should have a machine shop where they can fashion basic items like panelling, piping, basic components etc from materials in stock; perform basic repairs of some simple components; cannibalise damaged/broken equipment for spare parts; rewirring work; basic electronics repairs etc.