Yes your converter should charge your house batteries. Easily tested with a multimeter or at a minimum, functioning 12v items like lights, water pump etc. How long have you had this rv? I do find the question a bit odd because in 2024 you mentioned concern about keeping batteries charged in storage without being plugged in. So you, yourself said plugging the RV in charges the batts.
Right, I did say that, but I"ve always used a battery charger to keep the bank of batteries charged, assuming that my older converter didn't do this. Didn't seem like it did when it was plugged in, but my bat bank is rather large and I might not have noticed???? I just thought older converters didn't charge the battery bank. Is the charger on the controller a trickle? I guess I could just measure the bank, and then measure it plugged in to see a rise?
anything that puts out a voltage higher than the batteries will charge. the problem is different types of batteries take different charge voltages and profiles for optimal, or complete charging.
so what you need to find out is what the model number of the converter is and see what it is rated at. the problem with a lot of older converters is they were single stage. these worked, but when you are plugged in and the batteries are charged, they would keep outting out the same voltage and over time destroy your battery. newer ones are 3 or 4 stage, if you include the equalization fucntion and may even have selectors for charge profiles for different battery types. this is important because a lead acid battery requires different voltages in the charging stages than say AGM, or LiFePO4. these profiles are to ensure proper 100% full charges with out stressing the battery. a good old single stage like I had in my old truck camper would destroy a battery in 1 to 2 years if it was pluged in a lot. it got upgraded for a moderen power center.
