I'd like to see that, but considering it's not possible to independently validate this because you can't run anything else than WebKit, we have to take Apple's word for it. And I'm not sure I can trust them in that regard, it's more about control than performance. They don't want PWA to become viable alternatives to their apps, and controlling WebKit with an iron grip is a way toward that end.
Using Safari over Chrome or Firefox gains me 90-120 minutes more battery on my Macbook. Android went through contortions and re-architectures for over a decade to even approach iOS' place on the performance/battery-capacity/battery-life chart. I used to be an Android user and wildly better battery life (especially idle—I gather it's better now but damn Android used to eat a lot of battery while doing nothing) is part of what got me to stick with Apple, when I tried their phones. I'm fairly sure mobile Safari—and so, Webkit—is more battery-friendly than Chrome or Firefox.
