I converted my 2021 I3 last summer. I'm an electrical engineer, so it wasn't unfamiliar; but anything with an RV can be a mystery. Here's some background on things that were mentioned above....
You can swap-out the basic batteries with LiPO4 versions. In the existing stairwell, I have 610 amp hours (AHr) of capacity. The factory batteries offer 70? Ahr of capacity, so this is a huge upgrade (Lead Acid batteries don't like to be discharged farther than 50% where LiPO4 ones can use 100% each cycle without damage). LiPO4 batteries run a little higher in voltage than Lead Acid. They are more like 13.8V rather than 12V. You charge them at around 14.5V instead of 13V for Lead Acid. This little voltage difference is the source of all the remaining issues left to deal with. You can see that if you charge the new LiPO4 battery with a 13V charger, you won't get much charge in.
Therefore your charger needs to be LiPO4 compatible. In the 2021, this meant simply throwing a little DIP switch on the charge controller below the cooktop. If yours does not support the switch, you can simply buy a new charger module for that same power distribution box (from Amazon) and you'll be good to go in 5 minutes of replacement time. This will allow your 110VAC source to charge your batteries.
The next problem is that the way Lead Acid batteries are monitored for capacity is to simply measure the voltage of the battery. As it is drained, the voltage will drop from 12.5V down to 11.5V (rough numbers), and you can plot a line that translates that into fill level. This does not work on LiPO4 batteries. Happily, nearly regardless of fill level, the batter will still put out 13.2-ish volts. It is a very flat line so it cannot be used to estimate fill level reliably. Instead, there are ways to count the charge going in and out of a battery terminal to make a fill-level-meter. This is the SHUNT device that is mentioned. It is a device that sits in series with the electron flow in and out of the battery and simply keeps a count in and out and translates it to fill level. These are available on Amazon as well. I used a Victron one.
The next problem is charging your LiPO4 batteries from your sprinter alternator when driving. Alternators are, by default, setup for the Lead Acid charging voltage (some newer ones in newer Sprinter vans are a little more advanced and behave better with LiPO4 charging levels). As mentioned before, this is a little low for LiPO4 battery which would mean you might drive for hours, but you would never fill-up the battery. Further, an empty, large LiPO4 battery could draw A LOT OF CURRENT from an alternator causing it to heat up. A BIM (and a LiBIM) is a device that will connect the Sprinter's battery to the house battery when the house battery needs charging and the engine is running. The LiBIM includes timers to help reduce the problem of heat. This was not my choice. Instead, I used another Victron product that actually accepted the 12V Sprinter's battery voltage and DC-DC voltage converted it to the 14.5V charging profile of a LiPO4 battery. This device has a programmable current setting. This gave me the opportunity to both get a full charge and limit the heat/current I would draw from the chassis alternator.
Finally, there is the question of solar. It is not required. If you're going to drive a lot between stays, you could just use your alternator or plug-in (or generator) to charge your batteries. The 110VAC charger is around 60 Amps (840 Watts). The Alternator setup I have is rated at 50 Amps (that's 700 Watts). The battery capacity is 8,500 watts (in my case) so a half-full battery would charge by driving 6 hours. Putting solar on the roof gives you an independence from finding 110VAC somewhere or having to drive. Personally, I love having it. It also means that I NEVER have to worry if my battery is too low (or being damaged by over draining). Just sitting in my backyard, my RV keeps its battery charged (even in the winter shade). My Solar installation used 800W of CIGS solar panels (see Bougerv). My choice was driven by the fact that these were peel-and-stick to the roof and you can walk on them--so much better than screwing mounting brackets for hard solar panels. Driving down the road on a sunny day, I charge with both the alternator (700W) and the solar (another 700W) which means I can fill a half-drained battery in 3 hours.
Another thing I should mention is your Inverter. My rig came with a 2KWh inverter which is enough (if you're careful) to drive my air-conditioner/heat pump or my microwave oven for many hours. Honestly, we never plug in. You might consider swapping out your 1KWh one for a 2-3KWh one. This will mean you can warm-up your coffee in the morning without turning on your generator. Becky and I just got back from a Las Vegas trip. We camped in Mojave (Red Rock Canyon State Park) and at Circus-Circus (on the strip). We used battery to run our refrigerator and heated at night using the heat-pump. Virtually no propane used (except for hot water). We never started the generator and never plugged-in.
I would enjoy helping you understand each of these steps and guide you through you actions if you choose to take on this project. I chose a Victron DC-DC converter, Victron current SHUNT and Victron Solar MPPT charge controller. There are a little cheaper alternatives, but Victron is well-respected and they all share the same remote access via Bluetooth App on my phone.
Tom
Portola Valley, CA