On Fire TV, invoking Alexa and dismissing its overlay popped the profile
picker over a still-playing session: MainScreen treated every resumed
lifecycle event as an app open and re-applied "ask for profile on open".
The Alexa overlay only produces inactive -> resumed, which the handler
could not tell apart from a real return to the foreground.
Track the deepest lifecycle state since the last resume in a small gate
(ProfileSelectionResumeGate): only a genuine backgrounding (hidden,
paused, or detached) arms the prompt for the next resume. This also
keeps iOS working, where returning from the background arrives as
hidden -> inactive -> resumed.
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