If this works, then you know without a doubt you had either a file system issue, a system configuration issue, or a third party app was interfering.
Then only install StarCraft 2 to see if there are any issues. The easiest way to determine if there is a compatibility issue with macOS and StarCraft 2 is by performing a clean install of macOS by first erasing the entire physical drive before reinstalling macOS. It is unlikely you will find anyone who is aware of a StarCraft 2 specific issue on the general Apple forums. You can also contact Blizzard support or visit the StarCraft 2 game forums to see if other users can assist you in case the issue is with the game. If you still have issues, then run Disk Utility First Aid, otherwise it likely indicates you have some type of system configuration issue or an issue with another third party app. If you have these types of apps installed, then uninstall those apps by following the developer's instructions.
If your macOS boot drive has at least 20GB of free storage space, then make sure you don't have any anti-virus apps, cleaning apps, or third party security software since these types of apps are not needed on a Mac and they usually cause more problems than they solve.
Keep in mind even if you installed StarCraft 2 to the external drive the game will likely still use the internal boot drive to store game data such as temp & cache files which could add up to multiple GBs of data used on a drive that you indicate does not have enough free storage space. Your macOS boot drive needs to have at least 20GB+ of free storage space at all times so that macOS and all your apps are able to work correctly. If your macOS boot drive does not have enough free storage space, then macOS will not be able to run properly which also includes your StarCraft 2 game not running properly even if you installed StarCraft 2 to the external drive which has free storage space. You may have downloaded the StarCraft 2 installer to your external drive which has free space, but where are you installing the game itself when you run the installer?Įven if you are installing the app to the external drive which has enough free space you did mention your Mac boot drive (internal?) does not enough free storage space to install and/or download StarCraft 2.