Connecting a new Apple TV to a stereo and Tv

As I said, there are literally dozens of them available. Here’s just one example available from Amazon for $20

https://www.amazon.com/Optical-Toslink-Bi-Directional-Converter-Splitter/dp/B084T4QDFP/ref=sr_1_1_sspa?keywords=audio+optical+fiber+cable+to+hdmi+output+adapter&qid=1665180295&qu=eyJxc2MiOiIyLjA1IiwicXNhIjoiMC4wMCIsInFzcCI6IjAuMDAifQ%3D%3D&sprefix=hdmi+adapter+with+optical+out%2Caps%2C114&sr=8-1-spons&psc=1

Apple TV -> HDMI Splitter-> TV. Then optical out from splitter to your DAC. If you are connecting to a two channel stereo amplifier you really don’t need optical, you can buy a splitter with standard RCA stereo output.

Then unless your TV has an optical out you’ll need an HDMI passthrough/splitter adapter with audio output. Those can be purchased from any good audio shop, Amazon, and other sources.

So after the DAC where does the signal go for amplification and output to speakers?

New Apple TV models only have HDMI outputs. Please specify the make and model numbers of both your stereo and your TV so we can best advise you how to connect things.

Passthrough via the TV seems to be a good option for users that rely on optical connection to the audio system.