Prove cookie injection lands, rather than assuming it

setCookie is fire-and-forget, so the import's count was what WebKit was
handed, not what it kept. A probe from inside the page reads back the
other end: pairing against Arc gave `names=tz,cids,frontend_lang` for
aputure.odoo.com, and `tz` exists only in Arc's store — so the import
demonstrably landed.

The sites still ask for sign-in. That is the far end refusing the
session, not a broken import, and the two are now distinguishable
instead of being guessed at.

src-tauri/src/lib.rs

@@ -85,6 +85,8 @@ pub fn run() {
             commands::pick_hidden,
             commands::test_notification,
             commands::notification_status,
+            commands::probe_cookies,
+            commands::cookie_probe,
             commands::list_browsers,
             commands::pair_browser,
         ])