What hdmi cable does the latest Apple TV 2 nd generation need.

• The old 2010 Apple TV (2nd generation) has an HDMI 1.3 or 1.4 port (unspecified, but most likely) and that would work with any HDMI cable, even the old 5 Gbps “Standard” one.
• The new 2021 Apple TV 4K (2nd generation) has an HDMI 2.1 port, and could be best used with a 48 Gbps “Ultra High Speed” HDMI cable, to unleash all its capabilities.

HDMI cables - Different cable types - HDMI.org

It may be your HDMI cable or you may have a networking issue or to be honest a 2nd generation Apple TV is a pretty old device at over 10 years old! You may want to consider upgrading to an Apple TV4K model.

This is the cable for Apple TV 2nd Generation - Belkin UltraHD High Speed 4K HDMI Cable (2m)