No, the GoPro Hero13 Black is not compatible with the Rode Wireless GO II.
Rode Wireless GO II's wired outputs are 3.5mm analog and USB-C digital. GoPro Hero13 Black has no native 3.5mm or wired mic port -- its USB-C port is power-only and its only audio-input path is Bluetooth (for classic Bluetooth-audio devices, not Wireless GO II's RF transmission system). Requires GoPro's separate Media Mod accessory.
What works instead
See all compatible camera for the GoPro Hero13 Black →“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.”
“ith its 3.5mm analog and USB-C digital outputs, the Wireless GO II can record two individual channels of audio to DSLR and mirrorless cameras, iOS and Android”
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Confidence: high confidence