You can't over-charge a properly manufactured LifePO4 battery unless you go nuts and throw like 30V at it. This is because they are not simple "water tanks" for electricity like lead-acid batteries are. They have internal controllers that manage their state. In fact, they are not one battery. They are usually 4 (for a 12V battery) 3.2V smaller batteries wired in series internally (that's where most spec sheets get their 12.8V "nominal" voltage from - 4 * 3.2 = 12.8).
These internal cells actually need to be balanced as well, because it's bad for the performance of the battery if your cells are at, say, 3.1V, 3.0V, 2.9V, 3.2V. The battery management system (BMS) inside the battery handles this for you so you don't need to think about it (again, if it's a quality battery). In addition to managing charging, the BMS will do other things like cut off the battery if you short it (over-current protection), if it's too cold or hot (low-temp charging disconnect), and so on.
This is what a typical one looks like inside - you can see the four blue battery cells plus the charge controller and its four wires to the cells plus things like temp sensors.
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I don't know the battery you're referring to and it's not like there's a database of "well made batteries" to look it up on. Will Prowse on Youtube (among others) regularly does teardowns of batteries, and you might get lucky and find yours reviewed there. Even expensive batteries can be made badly, and he regularly will show things like poor solder connections, non-working temperature sensors, etc that can cause them to fail quickly even if they work at first. But let's assume yours is good.
For the BMS to do its job, it takes a bit of power itself. Think of two balloons. Connect them with a straw. The pressure between them will equalize and they will be the same size. Suppose you want to "charge" one balloon from the other. The balloon you want to charge from must start out bigger (a bit higher voltage) or the target ballon won't inflate. It will just sit there. To fill balloon A, balloon B must start with more air in it.
If the target balloon is very small (your RV battery is discharged) then any source balloon will inflate it - somewhat. This is what your current converter will do. If it puts out 13V and your battery is at say 11.8V, it will charge it at least somewhat. But to get it to 100% you usually need the charger to be at least 1-2V above the target you're trying to reach. The 12.8V rating on your battery is usually just a "nominal" value. To be at 100%, most "12V" LifePO4 batteries actually need to hit 13.6V. Your battery should have come with a spec sheet identifying its "boost" voltage, which is usually about 1V above that, or 14.4-14.8V (check your spec sheet).
There are add-on products that can help here, such as "DC to DC charger" units. Here's an example of one that lots of folks use in trailers where their trucks don't put out enough juice to charge their trailers while they drive:
https://www.amazon.com/Renogy-Battery-Batteries-Multi-stage-Charging/dp/B07Q5VYPCF
These options can help but aren't very smart. They won't hurt the battery because the BMS will protect it, but a proper charge controller designed for lithium batteries will give you more capacity per charge and more life out of the battery. Instead of just constantly supplying that high charge voltage, they'll run a charging "algorithm" that usually starts at some high value ("boost") and then drops to a lower one ("float") as the battery nears full charge
In my personal opinion (and worth every penny you paid), I think the best thing anyone can do when installing a lithium battery is add solar. MPTT solar charge controllers are designed specifically to deal with this challenge and to do it efficiently. They're usually very configurable, too, so instead of just setting a "lead acid vs. lithium" switch (like many RV converters sold today) you can set it up exactly per your battery's spec sheet and maximize your battery capacity AND lifetime simultaneously. They're cheap (many very good units run $80-$140), easy to install, and require no change to your existing converter. Plus you get all the side benefits - never a flat battery while your rig is in storage, extra power if you need to spend a night at a Walmart on a long trip (with no shore power or generator), etc.
You don't need 1200W of solar on your roof, either. These chargers are smart. If you're on shore power or a generator, and your converter is putting out 30A charging your battery, the MPTT will just contribute what it can. As your battery gets full to where your converter can't add more to the equation, the MPTT will take you over the top. Even a single 200W panel is better than nothing.