LibWebView: Do not block the console for the initial message request

If we set m_waiting_for_messages to true for the intial message request,
we might never receive a response, and block the console from requesting
any more messages indefinitely. Instead, issue a non-blocking initial
request, which is how the Qt and Serenity chromes behaved before the
ConsoleClient abstraction.

This also changes ConsoleClient::clear() to use run_javascript() rather
than js_console_input(), as that is also how the chromes used to behave.

Userland/Libraries/LibWebView/ConsoleClient.h

@@ -33,7 +33,6 @@ private:
     void print_html(StringView);
 
     void request_console_messages();
-    void request_console_messages(i32 start_index);
 
     void begin_group(StringView label, bool start_expanded);
     void end_group();