The Destiny 2 PC compatibility page states the following:
The following are examples of streaming applications which have features that are not compatible with Destiny 2.
OBS and XSplit The Game Capture mode of applications such as OBS and XSplit is not supported. The following methods are supported for capturing video
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OBS and XSplit The Game Capture mode of applications such as OBS and XSplit is not supported. The following methods are supported for capturing video