Freebox Remote, an unofficial remote control app for Android TV set-top boxes from French ISP Free, can act as a universal Android TV remote if you set the model to Freebox Pop while scanning. The app was recently updated to support the new Android TV Remote protocol v2, which is what the Google TV app's remote uses. Unfortunately, the developer told me he hasn't gotten keyboard input to work yet with the new protocol. Keyboard input does work if your TV hasn't received the latest Android TV Remote Service update, which supports the V1 protocol.
Since this app supports the v2 protocol, it should work with the Google Chromecast with Google TV as well, but I don't have one so I can't test it. I'm curious to know if it works!
You can download it for free from Google Play. There's a small IAP to remove ads and use widgets without restrictions.
I have no affiliation with the developer. I'm just sharing a cool app that a friend of mine told me about.
Seems like too much work.
FYI, Google TV app's remote control feature is for all Android TV devices, not just Google TV ones.
Also, the remote feature is available on the Google Home app as well.