fix: dismiss typeahead after launching session from floating results

When opening a session via the typeahead floating results panel, clear the
search query and active selection so the panel dismisses immediately.

Adds a test assertion ensuring the dashboard HTML includes the dismissal
logic after opening a tile.

src/webterm/local_server.py

@@ -904,6 +904,10 @@ class LocalServer:
         function openTile(tile) {{
             if (!tile || !tile.slug) return;
             window.open(`/?route_key=${{encodeURIComponent(tile.slug)}}`, `webterm-${{tile.slug}}`);
+            // Dismiss typeahead after launching from floating results.
+            searchQuery = '';
+            activeResultIndex = -1;
+            renderFloatingResults();
         }}
 
         function normalizeText(value) {{

tests/test_local_server_unit.py

@@ -257,6 +257,8 @@ class TestLocalServerHelpers:
         response = await server._handle_root(request)
         assert "/?route_key=${encodeURIComponent(tile.slug)}" in response.text
         assert "visibilitychange" in response.text
+        assert "searchQuery = ''" in response.text
+        assert "activeResultIndex = -1" in response.text
 
     @pytest.fixture
     def config(self):