You've misunderstood. Awareness absolutely is not "when thoughts come back online".
This is simple to experience for yourself since it'd mean we stop being aware when listening so intently thoughts stop. Obviously we don't cease to be aware at such times.
You've also misunderstood what is meant by nothingness ("no thingness").
Ok? I’m not an expert, but I’ve read enough to know that there are many differing takes on these topics within Buddhist thought. Your appeals to dogma are not convincing.
