What is this weird support line doing in this print?
I do not know the Qidi slicer, but if you look closely, you will see this line is thinner than the normal support infill lines. You could try to visualize the G-code in a viewer, usually this can be done in the slicer itself, but online viewers are available. The viewer will not only show the printed lines, but also show moves by the print head (usually in a different color). You can check whether this extra line is actually printed or a move. If it is a move, this extra line is caused by your hotend which is leaking when it moves. You need to properly tune the hotend with respect to the retraction settings and temperature. There are numerous retraction test print objects to find on the internet.

Depending on your slicer settings, some slicers are able to define where each layer starts printing (e.g. random, or start at sharp corner). The fact you see a support structure "printed the full height of the object" tells you that each layer starts at the same position. It is not uncommon in uniform simple parts where each layer starts at the same position (X/Y) as this is instructed by the slicer setting. In Ultimaker Cura such an option is called Z Seam Alignment.



Bottom line, all slicers will do this when your printer is improperly tuned (incorrect settings for e.g. print temperature, retraction, coasting, travel speed). It is up to you to find the correct settings, test print objects help you with that.