Ok I think I have a setup I'm happy with.
I bought a 100W Renogy solar panel for $70. It's mounted vertically on the side of the shed, roughly facing south.
Ecoflow delta 2 800Wh solar generator (already owned for camping, but was about $400). Placed on a shelf inside the shed, solar panel plugged directly in. I also have a River 3, which is like 220Wh. Either one works the same.
The Ecoflow is programmed to never turn off the 12V outputs. The shed 12V lighting circuit (made with RV lightbulbs inside, cheap 4x4 floodlights outside) is plugged into the Ecoflow cigarette lighter plug using the Ecoflow's own XT60 charging cord reversed. The lighting circuit used to run on drill batteries before this, and still has the drill battery input, so I can switch back to drill batteries if needed. Such as if I take the Ecoflow for something, I just plug in the drill battery so I still have lights.
Interestingly, the solar panel is a nominal 12V panel. So if I plug the solar panel directly into the lighting circuit, bypassing the battery and everything, it runs the shed lights fine just from the solar panel, assuming it's sunny out. Which is kind of fun but silly.
If I were starting from scratch, I could have wired the shed with 120V lights, because the EcoFlow has an inverter. But then for convenience, I would have to leave the EcoFlow inverter on all the time, which is less efficient, and would have to wire the shed lights to 120V standards. I actually wired the shed lights with standard 14ga romex and house light fixtures, even though it's 12V, but true 120V wiring standards would still require GFCI and a "real" breaker panel. The exterior lights are 12V LEDs which were dirt cheap compared to exterior 120V lighting, and this way I still have the drill battery option. If I ever run an electric circuit from the house to the shed, it will be an easy task to convert the shed to 120V.
In a normal winter day I get about 220 Wh of energy. One of the mower batteries are 240Wh each, so there's typically plenty of energy to run everything.
My Milwaukee 18V and Ryobi 40V battery chargers are mounted to the wall above the Ecoflow and plugged directly into the many 120V outlets on the Ecoflow. When full, the big Ecoflow has enough capacity to fully charge both 40V mower batteries, but this setup should would work with the smaller Ecoflow even if it can't charge the mower battery in 1 day, it should charge it before I need the mower again.
Whenever I put on a tool battery to charge, I just hit the inverter button on the Ecoflow to turn the inverter on. I have the Ecoflow programmed to cycle the inverter outputs one hour per day as a calendar task. So whether I remember to turn on the inverter outputs or not, the mower battery gets charged and then the inverter outputs turn off most of the time to save power. The tool chargers only pull about 300mW each when idling. Unfortunately that's too much to trigger any of the Ecoflow's "auto turn off" functions. It's still not very much drain though, so if I did leave the inverter on full-time, it would probably be OK. Also, I have programmed in a 30% "reserve" minimum charge level, just so that if solar is low or something, I'll keep 30% of reserve capacity in the Ecoflow so I can still override and have lights or whatever.
I have small 150W or 300W inverters for all of my drill batteries. So my whole tool battery collection is usable capacity in case of an outage. In theory, I could even steal back the energy from the tool batteries by using their inverters to re-charge the Ecoflow, but that would be a bit silly.
The best part of the setup is when I need the Ecoflow for something else, I just unplug it and take it. When I want to trim trees with my sawzall, setup my table saw or chop saw outside, power a work light, car battery charger, soldering iron in my neighbor's driveway, power the slow cooker for the potluck, radiant heater on the patio, or other things I used to run an extension cord from the house for, I just grab the Ecoflow instead.
The major flaw is the shed experiences extreme temperatures. The Ecoflow has a storage temperature of (14°F - 113°F), and I use it discharging down into the teens with no problem. But below 35C, it won't charge the batteries. This means on cold winter days it doesn't charge from solar. It's also not a problem because during the winter, I hardly use any power and the battery alone would last a week or two. But if I wanted to, I would put it in styrofoam cooler with a reptile heater and program it to keep itself warm.
