I bought a KSGER T12 about 4 years ago (has green circuit board) . It had worked fine but recently it started to make a very soft crackling noise inside and then the unit would turn off by itself and then turn back on.
Automatic turn off might be because of voltage-sense problems. There is an option in the menu about alerting voltage problems. Depending on the SW you might have a different GUI. In any case, the "V1" GUI has an option to display the DC voltage in the lower left instead of the selected tip.
Since the unit draws quite a noticable DC current, any soldering point is prone to get warm during use. They can oxidize, increase resistance and progressively make things worse. Soft crackling noise may be because of that, indication the final breakdown of the conduction.
Re soldering the junctions on the DC path might help. But you have to use a spare iron for that, not poking the live T11 back into it's case.

Is the old unit even worth fixing?
Hey, this is a place to discuss electonics and repairs. Name it your new project

Btw, "old unit". My trusty Weller W61C from 1988 is still in use. I had to replace the burnt mains filter capacitor and the heating element in the meantime. Probably because the mains voltage went up from 220V to 230V in the last decades. Still in production and spares are available.