Please specify the models amp and TV. It depends on their passthrough capabilities (usually listed in their manuals).
① If the TV doesn’t have support ‘PCM Multichannel’ audio passthrough,
and if the amp doesn’t support ‘4K HDR Dolby Vision’ passthrough,
then you may want to avoid passthrough altogether, by using an adapter that can split in HDMI 2.0 video and HDMI 2.0 audio: HDfury Arcana.
Apple TV →[HDMI]→ HDfury Arcana →[HDMI-video]→ TV
↘︎[HDMI-audio “eARC”]→ Yamaha amp
② If the amp doesn’t support ‘4K HDR Dolby Vision’ passthrough,
but the TV does have support for ‘PCM Multichannel’ audio passthrough (eARC),
then you can connect as:
Apple TV →[HDMI]→ TV →[HDMI eARC]→ Yamaha amp
③ If the amp doesn’t support ‘4K HDR Dolby Vision’ passthrough,
but the TV does have support for compressed ‘Dolby Digital 5.1’ audio passthrough (ARC),
then you can connect as:
Apple TV →[HDMI]→ TV →[HDMI ARC]→ Yamaha amp (with ATV set to Dolby Digital 5.1 output)
You will not be getting Dolby Atmos audio when a 7.1 amp is connected. Apple TV detects what connected equipment is capable of, and hides unsupported features. You would need an AV receiver that is Atmos-enabled to use that audio format.
You will only get 4K HDR Dolby Vision from Apple TV, when connected to a screen that supports 4K HDR Dolby Vision. Screens with more modest capabilities will cause the Apple TV to hide some functionality.
Use HDMI cables with bandwidth ratings that match the ports that they connect to. You do not want the chosen cable to be a limiting factor. The least of the ports and cables capability determines what bandwidth is available for content.
With HDMI 1.3–1.4 port on either side as lowest standard, 10 Gbps rated cables would be sufficient.
With HDMI 2.0 port on either side as lowest standard, 18 Gbps rated cables would be sufficient.
With HDMI 2.1 ports on both sides, 48 Gbps rated cables would support all HDMI 2.1 features.