PowerVR have open source drivers: https://developer.imaginationtech.com/solutions/open-source-gpu-driver/

but basically, yes convert the API calls into HW specific state and convert shaders to HW cpecific instructions.

For APIs like D3D up to DX11, the API tries to tell the driver everything it can about what it wants to achieve and then the driver translates that into whatever is best for the HW.

For something like Vulkan, the API tries to tell the HW what it has to do, leaving it much less room to do things in the best way for the HW although this does mean that the driver has much less work do.