Correct. There {may, should, might} be workarounds, but nothing definite available today.
Yeah, sorry, that was a bit brief. There are several options, depending on your requirements, skills, and available parts:
1) Connect the CV AC input to the grid. Leave the power on 24x7. Set the CV output to 52V (which is very approximately 25 percent charge on a 16S "48V" LFP battery). The 25% setting gives you some margin for power failures, and lets the solar system charge the batteries. Easy to do, but can be optimized below.
2) Connect the CV AC input to the grid through a relay. I used
https://www.amazon.com/gp/product/B07FCJFGL9 but anything that will carry the current and have a manageable coil voltage and available power supply. Use the inverter's "Generator Dry Contact" to power that relay whenever you want. For instance, when the SOC drops to 25%, the inverter "turns on the generator". When the SOC reaches 75%, it "turns off the generator".
3) Set the CV output voltage to 'fully charged', whatever that is for your battery system. Feed the CV Relay power in 2) above through some combination of computer-controlled relays and the inverter's "Generator Dry Contact". I'm going to be using
https://www.amazon.com/gp/product/B081RM7PMY connected to a Raspberry Pi that's already connected to the inverters for polling them for Modbus data. Wire things up so if the computer fails (or you unplug the USB to the dual relay), it'll default to Inverter Generator Dry Contact as at 2) above. Python code is trivial, though in my case the computer already is polling for Modbus data so it 'knows' SOC. Now you can get arbitrarily complex: "If the battery drops below some SOC based on load, environmental conditions, time till sunrise, expected solar power production based on weather, etc, turn on the CV until we reach 'some other condition'. If there's a hurricane coming, fully charge the batteries till the power fails. Modify rules based on house occupancy, etc.
4) Add 3-way toggle switch to 3) above for manual On-Off-Auto control as desired.
I'm currently at stage 1.5 above, and will be taking the parts down to implement the rest this fall. Your mileage WILL vary, and since this is a DIY forum, feel free to do anything else. Feel free to ask for clarification, and keep us up to date on your journey!
Since my CVs are plugged into the grid after the relays, it's trivial to fire up the generators, plug the CVs into the generators, and run them till they are out of fuel, which should(?) give me 10(?) KWHR of battery charge per tank of fuel for each of my two EU3000 generators.