I believe that you’re referring to privacy, not security here. And it requires logging on the server side. So if you set up your own server, that’s not a problem, and for those services that have integrated Wireguard, that’s up to them how they deal with that logging.

Saving battery life is not a “feature” as much as it’s a characteristic of the protocol. It’s much lighter and the connection much more efficient, so by nature it uses less energy than OpenVPN. I’m not sure how that’s a falsehood or dependent upon which phone you use?