When mirroring Macbook to AppleTV I get sound, but no picture.

Audio but no video probably means that AirPlay is unsupported in this (browser?) setup.

• Netflix actively blocks AirPlay, from any Apple device from browser as well as their own app.
• Amazon Prime Video has their own app in the Mac App Store. That will support AirPlay, although I can’t verify if that is supported for all models Apple TV as receiving device. It might be different for legacy models.
• Several other content providers also block AirPlay Screen Mirroring from browser access.
• Apple TV (3rd generation) has its own Amazon Prime Video app — until Feb 12, 2024. No need for AirPlay.
• Apple TV (3rd generation) has its own Netflix app. No need for AirPlay.

An HDMI connection from Mac to TV screen would be a supported method that doesn’t rely on AirPlay Screen Mirroring.

Else you may want to consider upgrading to more modern models Apple TV boxes.

apps and sites can block airplay mirror so if it's only with those 2 you get no visuals then they are likely blocking it, it's something apple honors

unless it's a such old apple tv it has not app store then you should be able to install a netflix and amazon prime app on it and view it without airplay being in the mix