Well, it is not exactly what I asked for, but some half-tweak.
Bike is not in the same room like TV. I have PC with large monitor.
I need to sync phone app and PC app. That is what zwift companion does for instance.
Your second proposal assumes that devices are connected to the PC. One of potential issues is a weaker signal between PC and devices.
I can reach a mouse from my bike, although it is not convenient during a ride. I can use it to start and finish. It is true you don’t need much of control during a ride, but… sometimes you do.
Also, I can install some touchpad app on my phone to control PC i don’t need additional device.
But possible device connectivity issue remains.
So, basically, those are all workarounds. As I understand, there isn’t a solution provided by Trainer Road.
As I already mentioned, I can live with that, I just want more convenience. 