Not sure what a TV hotbar is, but you’d have to figure out if this command is being sent via IR, RF, ADB, the remote API, or something Sony proprietary, and then figure out if it’s possible to call that from Home Assistant.
For creating new sources, see this thread: Android TV Remote - App Links/Deep Linking - Guide. I’m also not sure about 1:1 mouse control on Android TV. I know it’s possible on Windows using Unified Remote, but I don’t think the 1:1 mouse capability of that is possible on Home Assistant.