Learn Farsi: شایعه است که او با وسواس در زیرزمین نقاشی می‌کشیده است. - Rumor has it that he used to paint in the basement obsessively.

This is the Evidential Past Continuous. Because the sentence begins with شایعه است که (rumor has it that), it shows the speaker is reporting a habitual past action they didn't personally witness. To express this hearsay, Farsi uses می‌ + the past participle (کشیده) + the short copula (است).

How would می‌کشیده است typically sound in everyday spoken Farsi?

In colloquial speech, the final است is almost always dropped, leaving just می‌کشیده (pronounced 'mi-keshide'). You have to listen carefully for that final '-e' sound to distinguish it from the regular past continuous می‌کشید ('mi-keshid').

How does the phrase با وسواس work to mean 'obsessively'?

Farsi frequently forms adverbs of manner by pairing the preposition با (with) and a noun. وسواس means 'obsession', 'meticulousness', or 'compulsion'. Therefore, با وسواس literally translates to 'with obsession', giving us the adverb 'obsessively'.

If the sentence started with 'They say that' instead of 'Rumor has it', would the verb tense change?

No, it would stay exactly the same! Any phrase that sets up hearsay or reporting—such as می‌گویند که (they say that) or شنیده‌ام که (I have heard that)—triggers this same evidential verb form when describing a continuous or habitual action in the past.