fix: sidebar arrow hint stays visible until sidebar actually opens

Previously the welcome page arrow hid immediately when the extension's
content script loaded — but extension loaded ≠ sidebar open. Now the
signal flow is: sidepanel connects → tells background.js → relays to
content script → dispatches gstack-extension-ready → arrow hides.

Adds welcome-page.test.ts: 14 tests verifying arrow, branding, feature
cards, dark theme, and auto-hide behavior via real HTTP server.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

extension/sidepanel.js

@@ -1352,6 +1352,9 @@ function updateConnection(url, token) {
     document.getElementById('footer-port').textContent = `:${port}`;
     setConnState('connected');
     setActionButtonsEnabled(true);
+    // Tell the active tab's content script the sidebar is open — this hides
+    // the welcome page arrow hint. Only fires on actual sidebar connection.
+    chrome.runtime.sendMessage({ type: 'sidebarOpened' }).catch(() => {});
     connectSSE();
     connectInspectorSSE();
     if (chatPollInterval) clearInterval(chatPollInterval);