In what sense is ego actually just pure awareness?

In my previous article, In what sense is it true to say ‘everything is one’?, I wrote:

So Bhagavan is the ultimate reductionist: All phenomena are just thoughts; thoughts are just mind; mind is just ego; and if instead of looking at anything else we look keenly at ourself alone, we will find that ego is actually just pure awareness. Therefore pure awareness is all that actually exists: it is ‘one only without a second’ (ēkam ēva advitīyam).

In what sense is it true to say ‘everything is one’?

A friend wrote to me recently, ‘I think I got this part wrong: “Everyone is oneself”. You would say I am saying “Many is one”, right? What would you say? There is just one?’, in reply to which I wrote: