No, the DJI Mic 2 is not compatible with the GoPro Hero13 Black.
DJI Mic 2's wired outputs are USB-C, Lightning, and 3.5mm TRS -- all designed to plug into a port. GoPro Hero13 Black has no native 3.5mm or wired mic port on the body itself; its USB-C port is power-only and its only audio-input path is Bluetooth (for classic Bluetooth-audio devices like AirPods, not DJI Mic 2's own RF transmission system). Requires GoPro's separate Media Mod accessory to add a 3.5mm mic port.
What works instead
See all compatible microphone for the DJI Mic 2 →“MAGNETIC DOOR + POWER CABLE KIT The magnetic cable forms a weatherproof seal with the door and connects to any USB-C power source to continuously power your camera.”
“Mic 2 supports USB-C and Lightning outputs, as well as 3.5mm TRS analog output. It is compatible with most cameras, smartphones, and computers.”
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Confidence: high confidence