[FEATURE] Add keybinding action for /btw side conversations

Problem

The /btw command requires typing a slash and Latin characters. For users with non-Latin keyboard layouts (e.g. Cyrillic), this means switching the input language every time they want to ask a side question — which defeats the purpose of /btw being a quick, low-friction interaction.

Proposed solution

Add a bindable action (e.g. chat:btw) to the keybindings system so /btw can be triggered via a keyboard shortcut. For example:

{
  "context": "Chat",
  "bindings": {
    "ctrl+shift+b": "chat:btw"
  }
}

This would make the feature accessible without switching keyboard layouts or typing any specific characters.

Additional context

The current keybindings system already supports custom actions via ~/.claude/keybindings.json, but /btw is not exposed as a bindable action yet.