We only supported headless clipboard management in test-web. So when WPT
tests the clipboard APIs, we would blindly try to access the Qt app,
which does not exist.
Note that the AppKit UI has no such restriction, as the NSPasteboard is
accessible even without a GUI.
Clipboard handling largely has nothing to do with the individual web
views. Rather, we interact with the system clipboard at the application
level. So let's move these implementations to the Application.
You would have to just know that you need to define the constructor with
this declaration. Let's allow subclasses to define constructors as they
see fit.
Now that headless mode is built into the main Ladybird executable, the
headless-browser's only purpose is to run tests. So let's move it to the
testing directory and rename it to test-web (a la test-js / test-wasm).
