That sentence is a declarative sentence, a sentence that makes a statement.
He felt kind of sleepish.
he felt a kind of religious zeal.
Adrian never felt like she was in servitude as Kimberly's housekeeper, because Kimberly was so kind to her.
The bolded words "to unpack immediately" form an infinitive phrase, which consists of the infinitive "to unpack" and the adverb "immediately." Infinitive phrases can act as nouns, adjectives, or adverbs in a sentence.
It was weird, but it kind of felt like I was back in the future in my dream.
The kind of fish that has razor-sharp teeth is the barracuda.
'Immediately' is an adverb.
The adverb "immediately" describes "when."
sharp
sharp
A shark
Sharp