How to install and use photoshop on external SSD instead internal hard disk

In most cases, when you install an app one of the options you are given is the install location. The default location is the /Applications folder but in most cases when you run the installer you can specify a different location.

That said, imho it is not advisable to change the default install location.

FWIW, you will not save a whole lot of space by putting Photoshop on an external drive since it will still create massive support files that continue to grow as you use the app hidden away in the user's Library folder.

The only solution is to really get a Mac with a larger internal drive

Keep the apps on your internal and all the media etc. on the external.