Learn Farsi: این جنبش ادبی توسط وی گسترش یافت. - This literary movement was expanded by him.

The pronoun vey is the highly formal and literary equivalent of u. Like u, it is gender-neutral and means "he" or "she". You will almost exclusively see it in news, formal writing, or academic texts, which fits perfectly with this sentence discussing a literary movement.

Why does the verb gostaresh yaft use yaft (found) to mean "was expanded"?

The active form of this compound verb is gostaresh dadan (to give expansion / to expand something). In Farsi, you can often make these compound verbs passive or intransitive by swapping dadan (to give) with yaftan (to find). So, gostaresh yaft literally translates to "found expansion."

Is tavasot-e the standard way to introduce who did the action in a passive sentence?

Yes, tavasot-e is the most common way to say "by [someone]" when you want to include the "doer" in a formal passive sentence. Since Farsi passive voice usually hides the doer entirely, using tavasot-e lets you add them back in, much like "by" in English.

How is the adjective adabi (literary) formed here?

It is formed by taking the root noun adab, which means literature, etiquette, or culture, and adding the suffix -i to turn it into an adjective. It is linked to jonbesh (movement) using the invisible ezafe vowel, making jonbesh-e adabi.