you can download kodi and just play the mkv directly

Just download Kodi, VLC or any other media player and play it that way.

I have a Sony x850c with Android TV. It plays mkv files no problem. I just put the mkv files on a flash drive and plug it into the TV. The native video app plays them no problem. VLC and MX player are options as well.

Handbrake would be able to do that, otherwise you can install VLC Player on your TV which can play most MKV files.

Maybe cast it through VLC the or play it right through the Android TV version of VLC

Don't bother converting the video file to anything.

Just install VLC on your Bravia TV and play the 4K movie through that. You shouldn't have any issues.

Ah watta bummer. Got a 2TB External Hard Drive, got a 52GB movie, plugged it into my TV, doesnt read it

MX Player Pro or VLC can play mkv files just fine, though I'd recommend re-encoding it to x265 for better performance if you're playing the file over your local network.