fix(picker): prevent clearing input when chip menu opens

When a chip inside the picker has a menu (actions), clicking the menu
button would cause the picker to lose focus and clear its input field.
This happened because focus moved to the menu's portal, which is outside
the picker's DOM tree.

The fix checks if any chip menu is currently open before deciding to
clear the input field on blur. If a menu is open, we assume focus moved
to the menu and don't clear.

fix: #3676

Author: adrianschmidt-bot

src/components/picker/picker.tsx

@@ -547,9 +547,35 @@ export class Picker {
             return;
         }
 
+        // Don't clear if a chip's menu is open - focus moved to the menu's portal
+        if (this.hasOpenChipMenu()) {
+            return;
+        }
+
         this.clearInputField();
     }
 
+    private hasOpenChipMenu(): boolean {
+        if (!this.chipSet) {
+            return false;
+        }
+
+        // Query for any open menus inside the chips
+        const chips = this.chipSet.shadowRoot?.querySelectorAll('limel-chip');
+        if (!chips) {
+            return false;
+        }
+
+        for (const chip of chips) {
+            const menu = chip.shadowRoot?.querySelector('limel-menu[open]');
+            if (menu) {
+                return true;
+            }
+        }
+
+        return false;
+    }
+
     /**
      * Input handler for the input field
      *