Wave Link is a free program that allows you to pick and choose what apps in your system are heard by you as the host, versus people connected to your host. It also lets you create or hear microphones, which can be useful for some games. It’s similar to other apps like VoiceMeeter and VB-Cable, but has an interface that is easier to understand.
Download from their official site.
Wave Link does not work with Parsec’s built-in Echo Cancelling feature, so it should be disabled.

Wave Link’s interface is a grid, with your apps being the horizontal rows, and ‘mixes’ being the vertical columns.
As an example, this image shows how Wave Link would be set up to separate Discord and browser audio from the rest of the apps in your system. The host themselves get to choose what they can hear by adding these apps to the ‘Mix’. To hear a mix, ensure the blue ear icon is turned on.

Parsec can then capture either System (the default), Discord, or Browser.

Remember that, when changing things in Wave Link or in Parsec, it may be necessary to restart the apps you have modified. Parsec usually requires that you kick everyone from the stream for audio changes to apply. Discord may need to be restarted if you modify what group it is part of.