As determined by https://github.com/breunigs/bravia-auth-and-remote/.
Specifically, I followed the setup instructions in its README and then ran
curl --silent -XPOST http://192.168.0.131/sony/system -d '{"method":"getRemoteControllerInfo","params":[],"id":10,"version":"1.0"}' | pbcopy
(with the IP of the TV on my network).
I then ran its output through an online JSON prettifier.
I use this together with Alfred.app to bind functionality like power on/off to a Mac keyboard.