The most obvious tool Facebook has to track you is Apple’s advertising ID.
If it’s disabled or you said no when the phone asked you if you wanted to give the app permission to track you then Apple shouldn’t be sharing anything with them directly.
But Meta/Facebook has also been developing a number of workarounds or simply finding independent ways of tracking people.
Any website with Facebook tracking has access to your ip-address which can be used to identify your household somewhat reliably at a given point in time. So this doesn’t necessarily require Apple providing Facebook with anything new.
In iOS privacy and security settings there’s an option for an app Privacy report.
It takes a week to generate anything but lists every domain contacted by every app. This can help point out apps that use Facebook tracking.
You could also enable logging in something like NextDNS and use it with either the Apple TV or the phone.