Can Apple TV handle a TV signal from a settop box coming in?

Background

I am looking for a way to have my AirPlay2 compatible wireless speakers, combined with watching live-TV, and have no delay in the audio.

I recently learned that Apple TV hardware combined with AirPlay wireless speakers, is able to control synchronization between video on the TV screen, and audio on the wireless AirPlay speakers. Other combinations will cause a delay, where the sound coming from the speakers is behind what you see on the screen.

I also learned that there a re quite a number of TV's which support AirPlay, but only for streaming content from an iPhone/iPad to the TV. Not for streaming audio to AirPlay speakers.

What I try to understand

Assuming there are no TV's that support AirPlay for audio streaming to AirPlay speakers ...

Maybe it is possible to use an Apple TV connected to my TV, and have the TV-settop box of my provider hooked to an input of the Apple TV.

My question

1. Does the Apple TV have a Video In connection and can it handle video signal 'throughput'?
2. Does anyone know of TV's that support AirPlay for streaming audio to AirPlay speakers?

See picture for what I try to do.

Thanks @Urquhart1244 !

1 - If I find a TV with the 'app for Apple TV' does that TV then support streaming audio to AirPlay compatible WiFi speakers?

2a - That's what I expected, but good to have clarity, thanks.

2b - That's because I design & build wireless (active) speakers. My speakers use WiFi and can handle lossless formats such as FLAC.