This will be one of those where the details will change the answers for what might work the best but starting with a few details is also good!
No matter how we deal with storage, it takes some thought to get it right and preserve the batteries as long as possible.
Step one is that it does better if we can spend some time watching/checking how things are going. things that can slip up on us are not obvious.
One big thing is that even when we throw the battery disocnnects, the RV STILL has some drains on both start and coach systems.
Radio and ignition may drain the start battery. Safety items like CO and propand monitors are often left on as they don't want to risk that! The step extended may have a light bulb underneath that we don't see in the daylight!
Even when we are plugged in and all left working, the converter doesn't charge the start battery---if we don't make other plans to make it happen. Trik-L-Start is one popular item to think about. If we plug in for coach charging, a second small charger for the start battery is one way to cover for the second setup.
But that is not totally simple either because it may keep them charged but too well as it can run them out of water if we are busy, not watching close enough. That does kill batteries, for sure!
How much time we use it versus how much time we want to spent on watching or ssetting up for correct charging on both sets is one big item to think about but it does need some thought to do it the best possible. The books often say not to leave it plugged in for several reasons, one being that they assume we will not watch close enough and let the batteries boil dry!
So how often do you use it and how dedicated to being careful and watching the water and voltages?
I recommend leaving the inverter turned off when plugged into power as it uses battery to make the same power and no need to run if you already have the power. Inverter is for when you have battery but not 110AC power.
If wanting almost full time use out of the Rv, I leave the rest turned on and assume I will watch the water to keep it topped off and just assume the rest as a small price for the use. In use, the converter which charges the coach batteries willprovide most of the power for lights, fans, etc and the batteries are just kind of acting as reserve stored to make up any slack needed.
But if just used every few months for visits, etc. a different plan may work better and how much to adapt it may change for different times.
When stored, this was my situation and I did this. I like to go out and start the engine and run things once a month or so for a number of reasons. I want to know about rodents and leak problems before they get very big, so I start the engine and genset once in a while and run the air or heat, just to find out if things have gone wrong. I do this while I'm checking the battery water and looking around! Things that are not used often go down quicker than using them!
To keep from boiling the batteries to fast, I go for ading small disconnects on both sytems. These are easy to get to on my Rv and easy to turn to fully open ALL drains on the batteries.
https://www.autozone.com/batteries-s...E&gclsrc=aw.ds
Lots of different types but one of these on the negative/ground side of each battery will totally cut off all power from that battery!
Then when I'm checking the RV, I turn these on, start things and check the battery water and all the other points like looking at the roof, etc. while I let the engine and generator run for 1/2 hour or so to get them good and warmed up. I also check the battery voltage as an easy way to stop anything that might be going onwith them as early warning can prevent them going totally flat to ruin them.
No one firm answer is correct and it requires some though on what might work best for the amount of time you want to spend.