Voice still hoarse 4 months after vocal polyp removal?

It is likely that old habits die hard, so you might still have an incorrect and unhealthy voice production/breathing techniques, and that's why the sound quality has not improved. One of the core ideas for post-surgery voice therapy is to find correct and healthy ways to breathe and use the voice, sometimes that may take time but usually it should happen at some point. And, if the bad habits are still there, it does not remove the reason for the polyps so they will keep coming back unless the breathing and voice production techniques are correct and healthy again. Straining is indeed one of those bad habits, so it is a vicious circle situation. Please get a second opinion from ear-nose-throat specialist as soon as possible, surgery is always the last resort anyway so you might need some more time and some more therapy.