Learn Farsi: طراح داشت دنبال اشکال می‌گشت.

This sentence uses the past progressive structure you are currently learning: the auxiliary verb dâshtan plus the main verb in the past continuous. In Farsi, the auxiliary dâsht (was) usually comes early in the sentence, right after the subject, while the main verb mi-gasht (searching) stays at the very end. The object and other details go between them.

If gashtan usually means 'to stroll' or 'to turn', why does the translation say 'searching'?

The verb gashtan takes on a completely different meaning when paired with the word dombâl. The phrase dombâl-e [something] gashtan literally means 'to turn following [something]', but it is the standard Farsi idiom for 'to look for' or 'to search for'.

Is there an invisible Ezafe (an 'e' sound) connecting dombâl and eshkâl?

Yes! You should pronounce it as dombâl-e eshkâl. In this phrase, dombâl acts as a preposition meaning 'after' or 'in search of', and it requires the Ezafe to connect it to the noun eshkâl (flaw).

How do we know it means 'the flaw' and not 'a flaw'?

Farsi does not have a direct equivalent for the definite article 'the'. A noun on its own, like eshkâl, is often definite by default based on context. If the designer were looking for 'a flaw' (any unknown flaw), it would usually have the indefinite 'i' suffix added to it, making it eshkâli.