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/Infra/JSON.cpp

@@ -48,7 +48,7 @@ WebIDL::ExceptionOr<DeprecatedString> serialize_javascript_value_to_json_string(
     VERIFY(result.is_string());
 
     // 4. Return result.
-    return result.as_string().string();
+    return result.as_string().deprecated_string();
 }
 
 // https://infra.spec.whatwg.org/#serialize-a-javascript-value-to-json-bytes