It's very important to have a properly grounded soldering iron. Two reasons:
Reason one is safety ground so the tip/wand/enclosure does not become hazardous live if the power supply's insulation between primary-secondary fails. There is a risk with the cheap chinese power supplies having no safety approvals or certificates, and coming from the bowels of gaungdong that the insulation and spacings are dangerous.
A (certified) double-insulated rated power supply is not dangerous in this way, such as name brand laptop bricks. But this does not cover reason #2 for grounding the soldering iron.
Reason two is ESD or stray charge at the tip can discharge to whatever you are soldering to. Leakage currents from the power supply can put some potential at the tip/wand, compared to earth ground. This is very bad as even 10V can damage semiconductor junctions. The tip can float up to high potential say 60V due to the brick's internal Y-capacitance. Prove it by measuring ACV between jack barrel to earth ground with a multimeter.
Regarding grounding the KSGER and Quicko T12-clone soldering stations,
For the mains power supply (inside) units, the metal enclosure and rotary encoder body are not grounded.
The IEC power entry PE GND does have a (sometimes very thin) trace to DC(-), so the tip and controller are grounded, but not the metal case. I add a 18AWG wire from IEC GND to the chassis, solder it to the encoder tab as the encoder is bolted to the chassis. The encoder body needs a ground for ESD zaps.
For stations powered off a laptop brick, if it's a two-prong mains cord then you are in hell. You need to run a PE ground wire to the station. Clone manufacturers advise using an isolation transformer but that still is a problem, there can be stray leakage currents.
Another thread on grounding T12 stations:
https://www.eevblog.com/forum/reviews/how-to-get-rid-of-fluctuating-voltage-on-soldering-tip-(t12-clone-station)/