you should be able to turn it on via siri, you might need to adjust a setting especially if you are just using wifi on the TV, as I think the TV defaults to a "lower power - power off" which kills wifi.
In the TV's settings -- connection, mobile connection management, TV on with mobile. Make sure wifi is enabled. (your setting might be elsewhere, but look for similar words)
I've never been able to get siri to change the input directly, but you can record them into scenes.
There is a third party app called homebridge that makes non-homekit things work in homekit. With a plugin, it will control a lot of LG TVs. It allows you to set it up apps as inputs, so you could launch Netflix that way. You need a 24/7 computer and a bit of tech skills. (for what it's worth, homebridge on my older LG worked better than native my newer)
I'm not sure about the specifics of your TV, but you might be able to pair the AirPods with the TV, as most newer sets will let you pair bluetooth headphones. the paring process won't be as smooth as using the aTV, but it will work.
With the aTV, since your AirPods' paring settings are shared to all the devices signed on to your appleID, you just have to select them.
But no, you can't really control an appleTV with siri either.
On the siri remote, you can say "launch Netflix" but other than launching the app, there's not much to do. You can dictate searches instead of having to scroll-type them, but you have to manually navigate to the search field, then siri will convert your speech to text.
There is a "global search" that's available everywhere. You just have to press the siri button and dictate what you want to find. But Netflix is not included in that
In the shortcut app on iOS/iPadOS , there are appleTV actions, including power on/off, play/pause, and launch apps.
once again, for the most part you won't be able to control the app, once you've launched it.
So you could make a shortcut to launch Netflix. And if you setup a siri voice trigger, those would work from any apple device you have (not Mac though)
IF, the app has remote control functions, you might be able to do something besides just launching.
I have a couple apps (Plex, channels) that allow web control, so with both of those, I can use a shortcut to turn on the aTV, launch the app, then using web commands start certain media playing.