Hi jeyko,
Thank you for reporting this problem. Can you first check and let us know if the internal Remotly voice chat works for you?
Use the "Capture microphone" option in Settings->Audio & voice.
You need to enable the mic on host and client side to make both sides hear each other.
In this case after connecting to your friend you should hear only the system sound and the mic of your friend.
And of course your friend will hear you.
Is it not possible to route the Discord sound to a different audio device? It should be possible and this way the mic coming from your side would not be mixed with the entire audio of the remote PC.