iPhone not recognizing new cable

If you have multiple chargers, test the cable in them. If it still doesn't work, return it to where it was purchased and get your money back.

Look for an original Lightning cable, then you are sure it works. See a selection here:

Power & Cables - iPhone Accessories - Apple

If you try to play content from e.g. Netflix, it is possible that the content is DRM restricted. in iOS 16, some restrictions have been placed on which content can be played via the AV/HDMI lightning adapter.