Harry has just evaded pursuit:
フィルチやスネープの足音も聞こえなくなり、ハリーは落ち着きを取り戻しつつあった。
The sound of Filch and Snape's footsteps faded away and Harry was recovering his composure.
"Harry was recovering his composure" is a pretty clumsy but, I think, literal translation. I'm wondering just how natural 落ち着きを取り戻しつつあった is? That's not the main point of the question though.
This is my first encounter with V+つつある. I get the impression that it is a formal construct and wouldn't normally be used in speech. Is this correct?
I'm also given to understand that is is useful to replace V+ている to disambiguate between a progressive action and a change of state. Is this the only reason to use it?
Finally, I believe that V+ているところだ would also unambiguously imply progressive action. How would that differ from V+つつある?