Learn Farsi: پرنده هراسان در تاریکی پرواز کرد.

You absolutely could write پرنده‌ی هراسان (with the ezâfe) to strictly mean the noun phrase "the panicked bird". However, by dropping the ezâfe, هراسان acts as an adverb of state describing how the subject performed the action. A more literal translation of this syntax is "The bird flew, panicked, in the darkness." This is a very common and slightly more poetic structure in written Farsi.

What kind of word is "harâsân" and how is it formed?

هراسان (harâsân) is an adjective or participle of state. It is formed by taking the noun root هراس (fear or panic) and adding the suffix ـان (-ân), which indicates someone being in an ongoing physical or emotional state. You'll see this same suffix in words like خندان (smiling) or گریان (weeping).

Since this lesson is about narrative interruptions with که (ke), how would this sentence fit into that structure?

Because this sentence uses a completed action in the Simple Past (پرواز کرد), it perfectly serves as the sudden or interrupting event after که. To build the full structure, you just need to add a background action in the Past Continuous before it. For example: داشتم قدم می‌زدم که پرنده هراسان در تاریکی پرواز کرد (I was taking a walk when the panicked bird flew in the darkness).

Is the word تاریکی (târiki) related to the adjective for "dark"?