Although the sentence seems wrong to me, it is trying to say that while Naomi is waking up, she hears the sound of birds. The birds are not causing her to wake up - they are just there. The sentence seems wrong to me because the verb "awake" is not normally used this way. It is normally used as a transitive verb meaning "to cause someone to become awake". When I read "Naomi would waken..." it makes me wonder who it is that Naomi is waking up.

The sentence means that the birds would wake Naomi up. I can't isolate the meaning of "to" but "waken to" means the person woke up and the thing that follows happened at the same time. The thing that follows in the sentence (the sound of the birds) is assumed to be the cause of the awakening, but it isn't stated as such exactly. It is possible that Naomi may have been waking up already and just then the birds starting chirping. Does that help?

To means it was ongoing when Naomi woke awakened from sleep/slumber.

would 后面+ 动词原型呀！ 很明显是wake 呀！🙂

The sentence is fine English is flexible. Many people would insist it should be "woke up to the twitter of (the) birds". But no reason why it can not be plural twitters or twittering of (the) birds. Waken is past tense of to awake woke. so she Would waken. (the) is optional.