Are the "universal" laptop chargers safe / how do they work?
It is hard to comment on the quality of all "Universal" chargers, but they basically are selectable voltage SMPS which can be quite useful beyond just charging laptops which use another SMPS inside to regulated the charge of battery modes (CC , CV and off) and then another SMPS inside to regulate all the CV's required for all devices and MOBO.

They come in a wide range from 65W to 150W.

They are not designed to charge any batteries directly.

All the "Universal" types I have tried use remote voltage sensing at the plug with extra wires so that cable losses is nulled out.

I have used mine for dimmer control on 50W of LEDs with good results by figuring out the voltage bias control pin, Vref pin and ground.