This script tricks the tab into thinking it is visible, thus preventing the stream-quality from changing/downscaling as it would normally do 60 seconds after having switched to a different tab.

Thanks to CommanderRoot for maintaining this script since version 1.0.1

Update:
Since Firefox 109 you might also need to set widget.windows.window_occlusion_tracking.enabled to false in your about:config settings.
For Chrome you might need to set chrome://flags/#calculate-native-win-occlusion to Disabled