Regarding Internal Data for Apps downloaded on external drives

FWIW, most apps are hard linked to any of ~/Library/ApplicationSupport, ~/Library/Caches, or ~/library/Containers. Which is why symlinks to other locations don't work. There are some apps which know they will have large data requirements and will offer you to locate those files elsewhere. But I am guessing the app you have a problem with doesn't give you that option.

More often than not, because of large amounts of data that can be stored in those locations, installing the app itself on an external drive is not of much use in saving space.

There are three options, the last of which is not generally desired:

1. Move user libraries such as photos, music, and especially movies to the external drive. These three are generally large disk space users and don't need the speed of access of the internal drive. Also, look for other large files in your user folder as well and move them to the external.
2. Install macOS on a much larger external drive to give you space for everything. The caveats for this is that some macOS features are not available on eternal drives (Apple Intelligence, Wallet to name a couple)
3. Of course as stated initially his s the one you don't want to hear, get a Mac with a bigger internal drive.

Other than these three options, there's not much else you can do when you have low internal disk space.

Hello, how are you doing today? Firstly, you shouldn't install the OS to the external drive. I don't recommend it unless you absolutely need to do so (i.e. Running a virtual machine off of it). Second, to help you a bit better I need to know which platform you are downloading the game from and whether the drive is NTFS formatted or Apple formatted. If you are trying to download apps from the App Store to an external drive then the drive needs to be APFS. For Steam it's a bit easier, both NTFS and APFS work, but to my knowledge NTFS will be universal and should work on both Windows and Apple (so long as different games are used on different laptops).

I'm assuming you're using Steam so try this first, make sure your cloud data is synced and then uninstall the game. Go to the drive settings and format the drive as APFS. You may have better luck with that file system on Apple. Steam will still create a folder for you when you re-add the drive to the Steam launcher (if you are in fact using steam). Make sure to check that the drive you are installing is the correct drive. Reinstall the game. Let me know if this works and then we will go from there.