Star Trek: 10 Top Secret Artefacts At Daystrom Station
7. Borg Vinculum
Vinculum itself means "a connecting band of tissue, such as that attaching a flexor tendon to the bone of a finger or toe" which lines up with how such a device connects the Borg Collective and is well worth stealing as fans saw in the Star Trek: Voyager fifth season episode Infinite Regress.
For the Borg, the vinculum connects the minds of the drones together removing individuality and passing information among the hive. As Janeway puts it, "It brings order to chaos". For Section 31 this would be one of their must-have items without question. A vinculum would provide the best way to understand the links of the Collective mind and, as the episode showed, a possible way to bring chaos to order.
Such a device would also make a second appearance in the first season of Star Trek: Prodigy when Medusan Zero connected to one to find out how to deactivate a weapon integrated into the USS Protostar by the Diviner.
Just as with the instance in Voyager, the vinculum connected with Zero as it had attempted with Seven of Nine placing the crew in jeopardy - and aboard a Borg cube.
Neither of these vinculums ever made it to the Alpha Quadrant so Section 31 could have salvaged it from the remains of the Borg Cubes that did make it to Earth or maybe even from the Sphere that crashed in the Arctic.