How Toyota's eCVT transmission works: https://www.youtube.com/watch?v=ppyK3ZlUbtM (Nerd snipe warning: the Weber Auto channel is brilliant and has lessons about all kinds of transmission and engine types).

When it comes to something like F1 I think it's OK for efficiency to not be the top priority. Road vehicles absolutely should be as light and efficient as possible with strict limits on pollution (including noise). But it's OK for society to have a few things like F1 that are just for fun. We just don't want everyone to be driving F1 cars around their neighbourhoods or have an F1 race every week.

I think the F1 teams would all switch to racing versions of those transmissions the second they would be allowed to do so.

The efficiency gains wouldn't even be important in comparison (until you start bringing significantly less fuel than your opponents), but just the reduction in weight and size (important for aero considerations) would be worth it. Also, the power gains from always running the ICE (and its turbo) at the perfect sweet spot in the power curve would be a giant advantage in racing.

I believe F1 cars are actually incredibly efficient.

You can only take so much fuel and fuel is also weight. You can only win if you use the available fuel to propel you forwards efficiently.