Settings do not update when switching instance

CR: Version 2026.10.100, Beta 16, Channel Beta, Build 2875, Android 16 (arm64), Device Google Pixel 9a, Locale en-US, Push fcm, Flutter 3.47.9, Dart 3.13.7 Note: This issue does not seem to affect the desktop client, so I believe this may just be a visual bug on the mobile client rather than something with any functional impact.