Netflix uses Digital Rights Management (DRM) to protect content. In a web browser, this is done using EME (Encrypted Media Extensions), and uses DRM products such as Google's "Widevine" (found in Chrome, Firefox, Brave, etc.), and other technologies.
When connecting an external display or other device, these DRM technologies require those devices to support something called High-bandwidth Digital Content Protection (HDCP), which is an anti-piracy mechanism. It ensures the external device is "safe" and is not a recording device being used to duplicate the video feed. Many modern external monitors, TVs, projectors, etc. establish HDCP through an HDMI cable connection, and everything "just works."
I believe Apple's Sidecar feature works differently. Instead of sending a typical display feed to the iPad, it is sending an HEVC/H.265 video feed using technology similar to FaceTime video streaming. This is a non-standard/proprietary implementation for attaching a secondary display. It likely does not support HDCP and thus would be seen as an unauthorized display and probably why Netflix video playback stops working. I suspect the same issue arises with most other popular video services.
If accurate, it's unclear why Apple implemented Sidecar this way – maybe technical limitations with iPad hardware, USB-C/Wi-Fi, HDCP licensing fees, time constraints, or something else. I hope there's a path to a proper solution. Watching streaming video using Sidecar is definitely a big use case for me.