LibWeb: Implement quirks mode detection

This allows us to determine which mode to render the page in.

Exposes "doctype" and "compatMode" on Document.
Exposes "name", "publicId" and "systemId" on DocumentType.

Libraries/LibWeb/Parser/HTMLToken.h

@@ -174,9 +174,14 @@ private:
 
     // Type::DOCTYPE
     struct {
+        // NOTE: "Missing" is a distinct state from the empty string.
+
         StringBuilder name;
+        bool missing_name { true };
         StringBuilder public_identifier;
+        bool missing_public_identifier { true };
         StringBuilder system_identifier;
+        bool missing_system_identifier { true };
         bool force_quirks { false };
     } m_doctype;