what is the maximum resolution at which you can play games on playstation 4 pro?
If you set the resolution to [Automatic] your PS4 Pro system will default to the highest possible resolution available for the display device it is connected to and content being played/streamed.
Your PS4 Pro system should automatically enable 4K if it detects a 4K compatible device connected to it. To make sure 4K and the highest possible resolution are enabled:
PS4 Pro: How to enable 4K resolution