A nanny should be doing everything related to children. So children's laundry is fine, yours is not.
She should be looking up recipes and either buying the ingredients with money you leave or adding to a list for you to get so she can make them. Fishfingers and eggs are fine occasionally but not all the time. She has the whole week to plan what to cook. She can either do batch cooking and freezing to reduce time other days, or find healthy recipes she can do with little prep with children around helping, playing or when they nap.
She should be cleaning up after herself and children. So cleaning up after preparing meals, after children eating, after arts and crafts with them, children's books pola tidy and toys etc. All basically tidying and wiping, rather than actual cleaning.
She shouldn't be doing actual home dusting, hoovering, bathrooms etc. But if toddler wees on toilet seat of course a quick wipe, or crumbs in kitchen from children eating or mud in hallway from day out a quick Hoover of course.
She should however start the day with a clean home. So she should leave home how she found it. If she cleaned after herself and children evening before and left it clean, she shouldn't arrive to a home full of children's mess and yours created in the hours she wasn't there. If she does that's not her job to tidy or clean.
A nanny should also be teaching children to clean and tidy as age appropriate. Ie a toddler they would get to help them tidy toys before lunch and dinner with them, not nanny tidying everything alone for them. The same as children should be being taught to put their laundry in basket so it's easier for any adult to wash, and helping clear table from dinner etc, so you get teenagers who know stuff doesn't happen by magic.