I’m not sure if this is intended but it’s kind of annoying. The website keeps trying to get me to open in another application whenever I try to do 70% of the available things on warzone. Is there any way to fix this?

Install the app is the easy way. Seems to with IOS 12+. But not even profile pages or ladder pages seem to work without the app and that's defiantly an issue because the Warzone app uses more battery than Safari does. The Warzone app defiantly isn't energy efficient. Probably loads pages that it doesn't need to.

Battery usage is same for Android too, my phone gets hot whenever the app is left open

Maybe your browser has a setting for opening all webpages in desktop mode?