iPad as SideCar display blocks streaming of protected video on Mac.

Welcome to the wonderful world of DRM - Digital Rights Management. HBO, Netflix, etc., etc., etc. are the ones responsible for the blocking. They likely demanded compliance from Apple to not send their video streams to other displays. The iPad works wirelessly and the Mac is effectively streaming a stream and that is why it is blocked. You should be able to send DRM protected video to a projector or TV, etc. But you can't send it in other ways.

It is unlikely you are going to find a legit way around the DRM as the whole point is to prevent piracy and copying the content that is streaming.

So you are watching DRM protected video on a monitor and the iPad goes black? Yep, same DRM deal. It may also have to do with going full screen if the apps are not using the Apple fullscreen mode API calls but doing their own full screen mode which takes over all displays blacking them out.