The Student Room Group
Proud.
It means they realise their status and standing in life. Not necessarily proud, someone might be ashamed that they aren't worth more (richer, faster, stronger etc)

The negative connotation would be that they realise they have a low worth. Which may or may not be true.
Reply 3
Yes. It can be positive or negative.

Not really ashamed but they understand their limits.
Well, yes. Can be modest, arrogant or proud. But I assume from the context it means proud.