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The most obvious way to do this would be to ask for permission, but then it's likely every site would ask for it because it would be so lucrative. I'd would say that situation is worse than not supporting this feature, because suddenly having WM gives you a worse experience across the web.
I suppose we could have this as an option that the user can set on a site but the site can't prompt for. Where you can go into the URL bar or the extension menu or the settings or something and allow a site to monetize in the background. The site could prompt the user with instructions if it notices that it's been backgrounded and instruct the user to do this. Not sure if there's any existing features that work that way though. It could be a bit odd.