My Lidi stand alone induction hob is 2 kW with the default at 1 kW, it was used in my late mothers house as the halogen hob was useless, we selected the Silvercrest from Lidi as it has a knob to control it, many touch controls are not wheelchair friendly, they are invisible when seated that low.
I lived in a caravan for years on the building of Sizewell 'B' and understand the problem with in my case a 10 amp supply, it was a case of selecting low amp kettles, low amp water heaters, and converting a fan heater to 500 watt, even then I had the room thermostat with change over contacts so the water heater would only run when fan heater was off.
However I was told back then the mobile homes had to have a 32 amp supply, only the caravans were on 5 or 10 amp. It does seem each county council has "Site Licence Conditions for Permanent Residential Mobile Homes Site" and this can vary council to council, in the main the use of gas is what means they can work with a lower supply to many homes. The rules now require that a TN-C-S supply can NOT be used, the same as a touring caravan. The tourer normally has a battery, so a RCD or MCB tripping does not plunge one into darkness, the regulations say
Every installation shall be divided into circuits, as necessary, to:
(iii) take account of danger that may arise from the failure of a single circuit such as a lighting circuit
(iv) reduce the possibility of unwanted tripping of RCDs due to excessive protective conductor currents produced by equipment in normal operation
without battery power can't see how that would be complied with?
Most air fryer are 1000 to 1500 watt, but it seems the Ninja is often a lot higher so not suitable for caravan use.
There are special inverters, only seen them used with narrow boats, it allows one to use a small supply, typically with narrow boats 6 amp, and charge the batteries typical narrow boat would have 4 x 160 Ah, and use the batteries on peak demand, today there are also stand alone units with lithium batteries, these also allow one to power from low current mains supply or solar, and for a short time have a high power item running.
My own home has this, so although my DNO fuse is 60 amp, with the battery I can draw 72 amp, and if sun shining as well, around 90 amp. It is not designed with this in mind, it is just a side advantage of having solar panels and a battery, if the battery is discharged then there is no extra power. Units like this
can be configured to supplement your supply at peak demand times. The modern lithium battery will normally discharge 1/3 more current to what it can charge at, and a unit around 3.2 kWh will deliver around 3 kW and charge at 2 kW, so will discharge in an hour, and recharge in an hour and a half.