fix: send resolved sticker mode before auto to sync immediate state

Co-authored-by: Cursor <cursoragent@cursor.com>

frontend/src/pages/Picker.jsx

@@ -908,6 +908,9 @@ function Picker() {
                   key={opt.value}
                   onClick={() => {
                     setStickerMode(opt.value);
+                    if (opt.value === 'auto') {
+                      stickerSendRef.current?.(pollActive ? 'show' : 'hide');
+                    }
                     stickerSendRef.current?.(opt.value);
                   }}
                   disabled={!stickerWsReady}