Ok I am now a bit confused. F1TV app is still not available through Google Play on my Bravia TV and when I try to install it using phone or PC it lists it as unavailable for my TV. Then I had an idea to try downloading .apk file of F1TV app and installing it manually on my TV. So I downloaded the latest version of F1TV app from apkmirror, saved it on a USB drive, opened it on my TV using a File Explorer app, installed it and it runs normally. Opens up, logs in with my account and plays everything just fine.
So the confusing part is: if the app really works fine on smart TV why on earth are they making us go through all those hoops when they could just make it available like it is on android phones.