Hello,
Welcome to the Microsoft Community.
Edge and most Samsung TVs support Miracast, so protocol incompatibility is likely not the issue.
A message says "Not available for this site". Some websites are protected by copyright and do not allow casting. You can try casting other websites.
For this quesion:
Rather than casting directly from Edge to my TV, I'd like to know if there is a device that I could connect to my TV via HDMI, and then use Edge to cast to the TV through this device.
This might be what you want, but it's currently out of stock in Microsoft Store. You may need to look for this product on other e-commerce platforms.
Buy Microsoft Wireless Display Adapter - Microsoft Store
Best regards
Henry-N - MSFT | Microsoft Community Support Specialist