Does that work? I suspect the DRM content would not show.
Some streaming is not possible even when you can view it on the monitor.
I suspect that happens on the video driver or Windows rendering subsystem - where OBS would capture. I had issues like that trying to stream to my TV IIRC.
A quick search on OBS gives me - supporting my suspicion - https://obsproject.com/forum/threads/unable-to-record-hulu-and-other-drm-digital-rights-media-protected-content.130979/
A while ago when I last used it one of the two services worked while the other didn’t. Have you tried both?
Or are you using a webbrowser with no WebAssembly support or WebAssembly disabled?