Hey there, the other answer you got was wrong enough for me to register and chime in. There's no such thing as a BMS for lead acid batteries and no way to interact with their internal cells. What you're looking for is called a charge controller, it'll have bulk absorb and float stages just like your solar. As a rough rule of thumb, the amperage of your charger shouldn't exceed your batteries capacity in amp hours, slower is easier on them (but more run time on your genset so...)

The simplest and most common way to go is with an inverter/charger combo, I've never shopped for a standalone charger and don't have a specific reccomendation. You can totally get away with using a car battery charger though, especially if you're mostly using solar, and they are much cheaper. You can even use a welder, as long as you can set it to ~28.8v and an appropriate amperage (and put it on a timer, obviously won't step down on its own). My neighbor's using a charger from an old scissor lift, ~$200 on ebay, 25A/600w

If you got followup questions or more details on your setup I'm happy to help, good luck out there