If you are unfamiliar with OBS, it is an abbreviation for Open Broadcaster Software. This software is particularly useful for those who want to record gameplay and stream live.
The beauty of Discord is that it does allow you to use OBS and integrate it into the app. This will allow you to share your screen using OBS, but then use Discord to record the audio.
To do this, you will need to open Discord on your PC, and click on Sources, and choose the Desktop Audio option. This will enable you to have the audio from your stream and game to be available through OBS.
Once you have changed the settings on Discord, you will want to choose Desktop Audio 2 on your OBS settings, and apply it.