The PS5 controller needs to be wired and the Bluetooth must be turned off in order to play the PS5 version of the game on Call of Duty.
Cronus Zen Controller Adapter For PS3, Xbox 360, Xbox One, And Switch Wired/Wireless Keyboard & Mouse Support From Baiheyu, $139.65
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Wireless Convertor, Zen Controller, Cronus Zen Ps4, Cronuszen