The Script component from next/script is designed to allow for optimized loading of external javascript dependencies.
Loading javascript files from inside your application (/public/*) or outside should work without issue. Since scripts are loaded asynchronously by default you will need to account for that in Cypress commands that assert against side-effects of those script(s).
There may be times where a component loads an external script that is undesired during component testing - pulling in scripts can introduce undesirable side-effects and/or introduce unwanted external dependencies. This can be resolved by using cy.intercept to override the script loading; see mocks internal script test case in StateScript.cy.js for an example of this.