I'm sorry if this is a little too broad of a topic...
If you approach your question from a different angle it might end up being easier to understand. But first, let's clarify that a raspberry Pi can't use more than 15W of power at maximum load since its power adapter is rated at 15W. You almost got it right, its 5V @ 3A not 3V @ 5A. In reality it really can't consume more than about 7W at maximum load without any hats. So it will never consume 40W.
Now back to what you need, to do what you want. I really doubt you use more than 300W of power continuously in your tiny house. Your computer doesn't use anywhere near that amount. Unless you have a coffee pot running all day long or a space heater, or a television, or a large amount of lighting, I suspect you are averaging less than 300W continuously. Let's use some real world examples. I have a 55 inch 4K television that I use as my monitor to my multicore desktop computer. I don't have a graphics card in it. The combined power consumption of the desktop computer and the 4K television is less than 80W at normal load. That's typing and watching television on the computer. It goes up around 110W under moderate load and can exceed 200W combined at full load. So while you are working in the day without lights on, on your raspberry Pi4-B running at average load, you are using probably less than 75W of power depending on your monitor's needs. You can do that all day long with a single 100Ah battery. A 100Ah battery has 100Ah * 12V = 1200Wh of power. To be more specific, you can do that for 16 hours with a single 12VDC 100Ah battery assuming 100% efficiency, or for 12 hours assuming 75% efficiency. So you can easily get an entire day's work out of a single 100Ah 12V battery.
But average load isn't how you calculate what you need. You need to be able to run appliances throughout the day, and some of these have huge power needs. A microwave easily takes 1200W, even the smallest takes 900W. Toasters, hair dryers, space heaters, mixers, can easily each draw 1000-1800 watts of power while they are running. So you need to work out how many of those you will be using each day and how many of them you will be using at the same time. That will determine the size of the inverter you will need.
Also at night how many light bulbs will you be running? The average 60W LED light bulb today uses 7W. You can get 50W, 60W, 75W, 100W versions. You can even buy 12VDC versions of LED bulbs. If you choose to use 12V DC bulbs you don't even need an inverter to run them. You just connect them to your battery. I have AC lamps that I run 12V DC bulbs using a simple AC to 5521DC connector, that are 100W equivalent that use 12W of power, I can run them on an AC/DC adapter rated for 12V @ 1A output (12W) continuously. I don't need more than one of those. They are as bright as any LED plugged into AC. So get some of those and put them in a couple $9 lamps from Amazon and you will have all the lighting you need for 24W. You can run two of those for two days on a single 100Ah battery.
Do you have any 240VAC appliances? It doesn't sound like you have to run an air conditioner. Do you have a gas stove/oven or electric? Do you use a clothes line or an electric dryer? Do you use a washing machine, a dish washer, a refrigerator, a freezer, an iron, a hair dryer, a 3D printer, power tools, etc? Each of those may run several times a day but they do not run continuously. The average RV refrigerator uses about 1-1.5kWh per day. That means just for a refrigerator you will need 1000-1500Wh or a single 100Ah battery at least.
So you need to figure out what your real power consumption is going to be and what a modest expectation for power generation for solar will be to meet those needs. Then you need to size your battery bank to meet that at a minimum, and preferrable at least double that amount so that you have days you can use more, or so that you can use what you need when the sun doesn't shine as much. Like others have said, you will most likely need need a generator if you are going for the minimal solar inverter battery combination.
If you don't have any 240VAC appliances to run and nothing more than a refrigerator and small induction hotplate or something, you don't need to build like you would in a permanent residence. That means you don't need an 12kW hybrid inverter and 30kWh of battery. You can easily get by with the following:
400Ah@12V (3600Wh of usable power per day)
2500W (5000W surge) pure sine inverter
That's 225Ws continuous power for 16 hours a day, or less with bursts of large load for small amounts of time. An RV refrigerator will use 1000-1500Wh of that every day, leaving 130-160W for everything else. A mini fridge will do it for half that (550-850Wh/day)
A 2500W inverter with a 5000W true surge capability can handle anything you throw at it except air conditioning and industrial shop tools, but not everything at the same time. The total cost of these parts currently is around $900 (4 x 100Ah battery is around $720, 2500W pure sine inverter is around $160). Of course you can always spend more for name brands and larger components, but these prices are for parts I own and use. In a tiny home, where are you going to put the rack? Your estimate of $1250 for 200Ah@24V is equivalent in power but almost twice the price of the entire system here. You can configure four 12V batteries in 400Ah@12V or 200Ah@24V or 100Ah@48V.
You probably can get by with 6 solar panels rated at 300W or better if you can get 3 hours a day of direct sunlight on them, more if not. That means a fairly expensive solar charger. If you can find a comparable inverter/charger combo unit that is less expensive, then that would be a good modification. I doubt you will find one those that is less expensive than what I listed here. Make sure you get a real MPPT charge controller for whatever you buy. You can't afford to waste any power from your panels.
Again you will still need a generator to get you through the rainy days, but those are now the least expensive of any of the components. You can get a 5500W dual-fuel DuraMax generator for $550 or so. You would need 4 more batteries ($720 at least) for every day you want power without the sun, so a generator is a better option. (In fact it might be the best option since its the cheapest option for the most power)
If you decide to go with an off-grid inverter charger, then you really need to go with a 48V version. That will reduce the size and cost of your cables, will be a little more efficient, and you will find more options to accommodate that voltage.
Sungoldpower.com has a 48V 6000W off-grid inverter, charger on sale today for $850. I have a new one of those but haven't used it. Its supposed to be a decent starter unit.
I hope that helps.