There's eARC for signalling through HDMI, there's good ol' IR blaster.
For the Bravia, which is probably Android, you can likely write an android service that connects to the web and handles things like volume and maybe channels.
IR blasters are rough because there's no feedback. You're literally just shouting out commands into the void, and heaven forbid if it's something that's a toggle where you don't know which state you're starting from.