1. Open Discord.
2. If you want the Desktop Audio to not include Discord, you'll first have to tell Discord itself to output its audio somewhere else. Even if it's to headphones, for instance.
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3. From there, you can pick up Discord's audio by clicking on this + sign (Add Source) in OBS and then choosing "Application Audio Capture".
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4. Set that option to your Discord window and you should be good to go.