Learn Hardcore Turkish: Komşum çayı getiriverdi. - My neighbor quickly brought the tea.

It adds a nuance of quickness, immediacy, or doing something without fuss—often with a sense of “just went ahead and did it.” English paraphrases: “brought the tea right away,” “brought it real quick,” or “just brought it.”

How is the sentence built morphologically?

Komşu-m = neighbor + 1st person singular possessive = “my neighbor” (subject)
çay-ı = tea + definite accusative = “the tea”
getir-iver-di = bring + quick/just aspectual suffix + simple past = “(s/he) quickly/just brought”

Why is çayı in the accusative?

Turkish marks a definite/specific direct object with the accusative. çayı means “the tea” (specific). If it were indefinite, it would be çay with no accusative: Komşum çay getirdi/ getirdi = “My neighbor brought (some) tea.”

Is -iver- related to the verb vermek “to give”? Does it mean “gave”?

It’s historically the light verb vermek, grammaticalized as an aspectual suffix. In getir-iver-di, it does not mean “gave”; it marks quick/easy/spontaneous completion. Compare:

getiriverdi = “(quickly/just) brought”
getirip verdi = “brought it and handed it over” (two separate actions)

Is -iver- formal or colloquial?