In particular if I try to do some normal JavaScript things with window.opener's getter, it doesn't work. https://github.com/web-platform-tests/wpt/pull/15078 has tests. (I kinda expected this to already be reported. Chromium has a similar issue. But I couldn't find anything.)
We pass both the tests added in that PR. Could you please REOPEN this bug with details if you believe there is more to be done?