That looks really scary mate.
Not sure what to say really, but when I looked at the pictures first and before reading your post I straight away blamed the LED being left on for too long as they generate quiet a lot of heat quiet quickly.
Is 10min enough to cause this sort of damage, not sure, plus, I'm pretty sure the lights go off within 10min anyway

and I have noticed that few times, they wont stay lit for as long as you keep the boot open.
I have similar LEDs fitted and no issues for over 18months at least and I have them as interior lights as well which I've had on for more than 10min on many occasions.
Could short circuit cause so much damage on 12v supply?? I don't know, other more knowledgeable guys will answer this question.
And yeah, in my opinion fuse should go off, I've had fuse for whole interior illumination going off because of something not so dramatic, but first I would check what type of fuse you have fitted in there.
It's possible it happened before possibly because of the wiring fault and previous owner got feed up with changing fuse or had no similar amper one and put a 20A or 30A fuse on a circuit which requires lets say 5-10A
Very worrying and needs further investigating for sure
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2006 D3 S8 5.2 V10
Ceramic Brakes, Bang&Olufsen, DTV, DAB, Rear Camera, BT, TPMS, Soft Close, Auto Boot, AMI , 4 Zone AC, Home Link, All Electric Blinds, Fingerprint, Ski Hatch, Black Extended Leather, Heated Sport Seats, Alacantra, Carbon Trim inc Aluminium Pack 2.
2015 A3 S line 1.4 TFSI - for the missus to keep her away from my car.
Standard S-line equipment, no extras.
2006 D3 A8 3.7 V8 - SOLD but not forgotten