OP did not specify what services they were using. I assumed if they were interested in tinkering with this sort of thing, they probably host something like Plex or jellyfin.
Honestly I’d start looking for ssf/tiny PCs being sold off by local businesses. I’d be putting some sort of Linux distro on it. I’ve been meaning to check out a few projects like KDE Big Screen and others. Unless there is some sort of killer Android app you can’t live without.
I mean the pixel a series is great. I have a 6a and my wife has a 7a. But you’d have to compromise on the 3.5mm headphone jack and the SD card reader.
As previously mentioned the Xperia is probably the only option that meets everything except the price. Last I checked the Xperia is like $2-2.5k.
I wouldn’t recomend used that much as all phones basically have an expiry date with only having so many versions of android.