Auto Crop
Is the automatic crop option supposed to work when you have an object
in front of a fairly standard background? I don't think I've seen it
work. The intelligent scissors tend to get most of an objects but with
lighting being variable it's never as easy as a manual crop.
Several different ways to extract a foreground other than the scissors tool. As you say if the background is complex then the colour or fuzzy select tools might only do a partial selection. But that might be enough combined with the quick mask to paint in 'missing bits'. You should also consider using a layer mask to the same effect.
Then the paths tool, often overlooked, but for smooth edges gives a good selection. A bit labour intensive.
The most automatic is possibly the foreground select tool.
https://docs.gimp.org/en/gimp-tool-foreground-select.html
Made my rough selection around the area and painted in the area. https://i.imgur.com/CxactcJ.jpg
Gives a selection like: https://i.imgur.com/GVImhkI.jpg
But that is not the same as an Auto-Crop: https://i.imgur.com/SXk44fG.jpg
There are plugins to assist, in particular I find the g'mic plugin www.gmic.eu with interactive foreground select useful.
rich: www.gimp-forum.net