Navigating Iraqi Kurdistan: Best public transport options for smaller towns?

I'm planning a solo backpacking trip to Iraqi Kurdistan next month and really want to explore beyond Erbil and Sulaymaniyah, hitting places like Amedi, Rawanduz, or Akre. While inter-city taxis are an option, I'm hoping to find more budget-friendly and local public transport, like shared taxis or mini-buses, to truly experience the region without renting a car. Any reliable routes, apps, or essential local tips for getting around efficiently?