You have options; there is not one single way to do this.
One option is to make the entire external drive bootable.
Another option is to boot from the internal SSD and put your User Home directory on the External. If you do this, then the 120 GB or so of System files will be on the internal and not on the external.
If you boot from the Internal and keep your Home directory on the External, where will you put your Applications? You have a choice: Internal or External. On MacOS, there is a /Applications and a ~/Applications directory. The ~/Applications is inside each user’s home directory. When you view your Applications, you see a combination of the Applications installed in /Applications and ~/Applications.
With a 256 GB Internal, you will probably have room for the System and also the Applications all on the Internal, unless you download massive games. If you want your Applications always installed on the External, then limit your account permissions and then Applications will always be automatically installed on the External, inside your Home directory, which is ~/Applications. If you give your account Admin permissions, then applications will be installed on the internal SSD at /Applicatiohns.