Atten 8586, is the wiring ok?

[ElectronicSailor]

I recently started to do some things with my atten 8586 since its performance was quite subpar. Installed a new clone iron with the shorter sleeve without holes, so that original hakko t18 tips fit.The stainless steel heating element was thankfully also a bit longer on the new iron.

The heat transfer improved quite a bit:
Before 370deg on the station - > 290 on the tip according to my fake hakko solder thermometer.
After,   315deg on station - > 295deg on the genuine (more tighter fitting) tip.

Next step would be to check the wiring, since I stumbled upon this thread here that talked about some issues with the wiring of 8586 units.  https://www.eevblog.com/forum/blog/eevblog-167-atten-858d-hot-air-rework-review/msg101436/#msg101436
I'm quite a beginner with all this. Regarding the topic I linked....
It seems on my unit the earth is attached  to the case. However on the image of the fix that was posted, I see that an additional wire was attached to the transformer. Is this necessary, since the transformer is screwed to the case floor, shouldn't there be sufficient contact with the wire that is attached to the other part of the case. I assume the additional wire was done as a safety measure in case there is no tight contact with the part of the case with the earth wire attached ?

What do you guys think ? If you notice anything that seems off or could be hazardous, please let me know. Thank you

Chinese equip, good value for the money, but most of the time always something to fix....