Learn Italian: Il pittore era triste quando ha finito l'opera. - The painter was sad when he finished the work.

This sentence perfectly shows how the two past tenses work together! We use the imperfetto (era) to describe an ongoing state, feeling, or background condition in the past ("he was sad"). We use the passato prossimo (ha finito) for a single, completed action that happened in that specific moment ("he finished").

Could I use the passato prossimo and say è stato triste instead of era triste?

You could, but it changes the meaning. Era triste describes his ongoing mood at that exact moment, without focusing on a beginning or an end. È stato triste implies a completely finished period of sadness (for example, "he was sad for two days"). When describing how someone felt when another event happened, the imperfetto is the natural choice.

I learned that verbs of motion or change of state take essere. Why does ha finito use avere?

The verb finire (to finish) is a special verb that can take either helper verb depending on how it's used. Because the painter is finishing something (a direct object: l'opera), we use avere. If there was no direct object and the work itself was finishing (like "The play ended"), you would use essere and say L'opera è finita.

Does l'opera mean the painter was working on a musical play?