You've got a lot of important considerations there. Given your requirements and budget, I would personally advise against an Ecoflow system. They are quite handy and portable, but in terms of value for money and customization, a DIY inverter/trolley system could probably serve you better.
Regarding the load, it is challenging to provide an accurate estimation without knowing the exact energy consumption of your devices. This is particularly true with fridges, as they can have unexpected spike draws. As a result, I would strongly recommend measuring the load using a Kill-a-Watt or similar power meter. This will help you get a more precise idea of your energy needs.
For your ONT/router, instead of running them off a larger system, consider purchasing a dedicated mini-UPS or two. They are affordable, efficient and designed specifically for these types of devices.
The kettle is a tough one. While I understand its importance, it's also a significant power draw. Gas is indeed a better bet. If it's necessary, you might look into low wattage travel kettles as a more energy-efficient alternative. More on this in a moment.
Lastly, for your budget, you can forget 24V, although I have to agree with
@TheChamp that is the best way to go.
Anything smaller is only good for running a TV and a few lights. Looking at a 12V/1000W inverter 'trolley' with a small lithium 100ah battery e.g., this
Axpert trolley might fit your budget, but is limited in what it can offer you. The capacity alone on the battery is 12V * 100ah = 1200Wh. Ignoring any inefficincies for a moment, even your small 650W travel kettle, will take a good 5-10 minutes to boil 500ml, using a good 650w*10minutes=108wh, almost 10% of the capacity of the system in one swoop.
My 58" TV, PC, and a few lights use about 350W. The above system would only give me a runtime of 1200Wh/350W=3.42 hours till you have a flat battery - never good.
So you need to adjust these figures. On lithium one aims to never use more than 80% of the capacity. So 1200Wh becomes 960Wh. Then you need to adjust it for the inefficiencies of the inverter (usually about 85%). Now we are down to just 816Wh of capacity. Lets deduct the 108Wh that you will use for the kettle, leaving you with 708Wh. 708Wh/350W=2.02hours of runtime. Not nearly enough, but can be done.
Foget the kettle, fridge, and run the TV at a lower brightness, turn off the soundbar and extra lights, and you can easily survive with 1200Wh for 3+ hours, if not 4.
