keybindings.json not working in desktop app (macOS)

Description

Custom keybindings defined in ~/.claude/keybindings.json have no effect in the Claude Code desktop app on macOS. They only work in the CLI.

Steps to reproduce

1. Add a custom binding in ~/.claude/keybindings.json:

{
  "bindings": [
    {
      "context": "Chat",
      "bindings": {
        "cmd+shift+x": "chat:cycleMode"
      }
    }
  ]
}

1. Restart the desktop app
2. Press Cmd+Shift+X in the chat input — nothing happens

Additional observations

• The default Shift+Tab binding for chat:cycleMode also doesn't work in the desktop app (it behaves like regular Tab)
• The built-in Cmd+Shift+M opens a mode selection menu but does not cycle — you still need arrow keys or mouse to pick a mode
• A true cycleMode action (press once to switch to next mode) would be very useful for keyboard-driven workflows

Expected behavior

keybindings.json should be respected by the desktop app, or at minimum chat:cycleMode should have a working default shortcut that cycles through modes without requiring a menu interaction.

Environment

• macOS (Darwin 24.6.0)
• Claude Code desktop app (latest version)
• Claude Opus 4.6 1M