I don't understand the function of как in this sentence:
Возле окна — большая клетка Букли. Сейчас она пустая: Букля уже два дня как улетела.
I know there a usage of как with perfective verbs that means "suddenly." However I wonder if here it isn't "approximating" two days: about two days ago.
This is unrelated to the как that expresses suddenness. And approximating two days would be an entirely different construction: Букля улетела дня два назад.
In phrases like this one, как serves to further stress that the time elapsed is the focus/"rheme"/new information communicated by the sentence.
This как refers to уже два дня, not to the verb.
[Вот] уже period of time как means 'it's already been period of time since', and "Букля уже два дня как улетела" means 'it's been already two days since Buklya flew away.'
There is a certain colloquial trend where conjunction как replaces когда. E.g.
Как дойдёте до перекрёстка, поверните налево
(I think I can see a direct analogy in English: When you reach the junction turn left => As you reach the junction turn left - is it a contraction of as soon as?)
I am not sure as to the reasons for this phenomenon but the following excerpt from Lermontov's well-known pastiche indicates that some historical process may be at work here:
Как сходилися, собиралися
Удалые бойцы московские
На Москву-реку, на кулачной бой,
Разгуляться для праздника, потешиться.
So I am tempted to hypothesize a transformation:
Прошло <уже> [a period of time] с тех пор (с того момента) как (когда) [the event happened] => <уже> [a period of time] как [the event happened] => [the event] <уже> [a period of time] как [happened].
I would also argue that this usage does preserve a certain shade of suddenness or rather instantaneousness of the event or the particular moment. One would say Как вошёл я в ресторан, сразу увидел Сашу, but never Как жил я Москве, каждый день ходил в Большой. Only когда will be used in the latter case. The escape of a bird lends itself very well to such suddenness.
It is also worth adding that с тех пор как is a stable and actively used idiom.
