Typing goes into the message box after switching from emoji search to another picker tab

Typing goes into the message box. This is similar to another bug but slightly different, but may have the same root cause https://feedback.fluxer.com/p/1622

Beta 60, Version 1.0.0, Android 16 (arm64), Device Google Pixel 9a, Locale en-US, Push fcm, Flutter 3.44.2, Dart 3.12.2

Expected behaviour Typing should go into the respective new search box.