Yes you are right, it was the expected flow but it was changed recently because users were not downloading the file after conversion creating unnecessary load and later at download stage the sponsored page was bypassed. Now the file is served after confirmation.

Is it correctly?
As I understand, “ok”, means that I can download converted file just now.
“processing” means that I need to wait a little time.
And “fail” would mean either non-valid url or a scheduled broadcast.

In addition, in the last month “processing” did not appear at all.

It is because of the information provided by YouTube.
OK status means valid video url.