Everywhere: Rename to_{string => deprecated_string}() where applicable

This will make it easier to support both string types at the same time
while we convert code, and tracking down remaining uses.

One big exception is Value::to_string() in LibJS, where the name is
dictated by the ToString AO.

Userland/Libraries/LibWeb/HTML/BrowsingContext.cpp

@@ -512,7 +512,7 @@ DeprecatedString BrowsingContext::selected_text() const
         builder.append(text.substring(0, selection.end().index_in_node));
     }
 
-    return builder.to_string();
+    return builder.to_deprecated_string();
 }
 
 void BrowsingContext::select_all()