Discord is the platform ... this feature ensures unwanted sound never escapes through your mic unless you want it to. Enable this feature by going to Settings > Voice and Video > Push to Talk.
It's best to restart the application and Discord ... and then return to Discord and fix its audio settings. Reboot Discord (and maybe your computer for good measure), start the stream up again ...
Instead of sharing your Max password, you can stream content on Discord and get a watch party going within minutes. And the best part ... “Also share application audio” is checked.