[FEATURE] Add `app:compact` bindable keybinding action

Preflight Checklist

• [x] I have searched existing requests and this specific feature isn't currently tracked by an open issue
• [x] This is a single feature request (not multiple features)

Problem Statement

The keybindings system (~/.claude/keybindings.json) binds keys to a fixed enum of built-in actions (app:toggleTodos, chat:externalEditor, etc.). There is no action for compacting the conversation, so /compact cannot be bound to a key or chord. Users who compact frequently must type the slash command every time, and /compact (a harness primitive) is also unreachable from custom commands, skills, and hooks.

Proposed Solution

Add a bindable app:compact action to the keybindings action list (Global context), so users can do e.g.:

{
  "context": "Global",
  "bindings": { "ctrl+k ctrl+c": "app:compact" }
}

Invoking it would trigger the same flow as typing /compact. Optionally accept the same free-form instruction argument that /compact <instructions> supports (not required for a first cut).

Alternative Solutions

• Type /compact manually (current state).
• Rely on autoCompact threshold — but that's automatic/mid-session, not an on-demand manual trigger.

Priority

Low/Medium — quality-of-life for heavy users.

Feature Category

Interactive mode (TUI) — keybindings.

Use Case Example

I compact at natural breakpoints many times per session. A single key chord is much faster and less error-prone than typing the command each time.

Additional Context

This is not a duplicate of the following, which the auto-triage bot previously conflated:

• #40837 ("Ask user whether to compact or quit") — about prompting the user at autocompact/exit time. Closed as not_planned. Different mechanism.
• #43195 ("compact-on-exit setting and app:compact keybinding action") — requested this exact app:compact action bundled with a separate compactOnExit setting; it was auto-closed as a duplicate of #40837 (an imprecise match) and is now locked.

This request is deliberately scoped to only the app:compact bindable keybinding action — nothing about exit behavior — so it can be evaluated on its own.