Does it really have that kind of self awareness to be able to do that successfully? I feel very sceptical.

I doubt self awareness has anything to do with it..

What else would you call the ability for it to adapt a task for its own capabilities?

Language modelling, token prediction. It's not much different from generating code in a particular programming language; given examples, learn the patterns and repeat them. There's no self-awareness or consciousness or understanding or even the concept of capabilities, just predicting text.

Sure but that kind of sounds like it is building a theory of mind of itself.

If it does have considerable training data including prompt and response when people are interacting with itself then I suppose it isn't that surprising.

That does sound like self awareness, in the non magical sense. It is aware of its own behaviour because it has been trained on it.

Just have it write 10 and bench them against your own.