How do I move the Applications folder that holds applications to an external drive?

Usually the most space is taken up by the Pictures and Music folder if you have large photo and music libraries. What I've done is create a Pictures and Music folder on the external drive and copied the contents of those files on the internal drive to them. I make sure the libraries were working before I deleted them from the folders on the internal drive. I then removed the Pictures and Music folder from the Finder's sidebar and dragged the Pictures and Music folders from the EHD into the Finder's sidebar. If you have a very large Documents folder you can do the same with it.

You can’t do anything with /System/Applications. It is mounted on the read-only Sealed System Volume.

I can’t imagine you have so many apps that they take up much space. What is the purpose of moving them?

If you are looking at the size presented for the Apps in the manage storage displays, that shows the size of the data created by the app, not just the size of the app. Moving the app won’t move the data created by the app.

In the context of the Information provided - Snow Leopard OS X 10.6 ?

Adopting that method from Snow Leopard released in 2009 to Ventura released 2022 is somewhat ill-advised for reasons already presented.

Yes, some Applications, in the Microsoft Windows Environment, can be assigned to install on an External Drive but that is Microsoft Windows not macOS from Apple

The data is stored wherever you create files using the app. You can move that wherever you'd like. The "data" is your files.