I was able to cast a HE dashboard (or almost any website) to a Google Home Hub using CATT. It allows touch control back to HE.
Sorry for the bad video, I compressed it to share in the post.
Here is the app used to make it happen. I was able to get it working both on Windows (using bash) and in Ubuntu. It's on a Home Assistant thread, but I didn't use Home Assistant.
Wow, CATT works great! I just installed in on my rPI and after a little learning curve, I now have my dashboard on my Nest Hubs. Will try to make an app for this soon. 
Sooo many possibilities! lol
Great find, @AndyM
I'll definitely be taking a look at this!
Credit actually goes to @kevin.
He has something similar going on directly in Home Assistant (not sure it has touch capabilities yet). As I don't use HA, he suggested I give this a try.
I'm not sure the implementation yet... If you ask the google home questions it will go back to the cast. But playing music or video will of course break the cast. I'm thinking a virtual switch, activated by voice, to cause CATT to re-run the casting request. Or also, the switch could be triggered by watching a custom attribute on the home for media being none (nothing playing).
Any suggestions on how to trigger the CATT command on the linux/windows machine from HE? I'm guessing it would be easy enough, but not exactly sure where to start.
NodeRed would be your best bet I think. I have the websocket connection already setup in Nodered so I would just need to filter a particular event and have that connect to an Exec node to run the script.
LOL, another thing for me to learn. I'll have to check it out.
Not knowing linux (or having anything running linux), getting this going was a bit of a challenge... mainly because I wanted to see if I could get my home remote dashboard (which runs on android) to it. I can, but... involves an android emulator running Home Remote, and a VNC app also on the android emulator, then running NoVNC in Linux to convert the VNC to HTML5, and then using CATT on the HTML5 site to the Hub. Multiple nights, but it is working... if for nothing else than to prove it could be done.
I suppose, using that method, you could actually "run" a lot of different android apps from the Hub.
Started playing with some code today...
I can now control CATT with HE through Telnet 
Now to have some fun, lol.
1st release of a working driver... 
You had me at “ANY web page”. Sounds great!
I must say I am intrigued by this. I however have no nest hub. I do have a show though
I know amazon recently got an a official youtube app finally. Is it possible this will work to cast there?
Edit. Just saw the youtube app does not seem to be available for the show.
I know that this is an old thread, but have a look at assistant-relay. it uses CATT to cast but can also communicate with the assistant for commands and broadcast. all this by http POST.
If you want CATT integration, you have to get the beta version. runs on RPI and most linux distros, I run mine on ubuntu.
I know this is a pretty old thread, but did you successfully do a website cast with assistant-relay. If so, what do you send to the device? I use the GAR to cast announcements, etc, but I was unable to figure out how to cast websites.
Answer my own question. Issue is catt converts the device name to lowercase. So "My Display" needs to be "my display" in Google Home.
Download the Hubitat app
