[FEATURE] Include session compact count in statusline JSON input

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

The statusline JSON input provides session metadata and context_window data, but there's no way to know how many times the current session has been compacted. Users building custom statuslines must resort to file-based workarounds using SessionStart hooks with "matcher": "compact", which creates a race condition: the statusline renders before the hook writes, so the compact count is always stale until the next render.

Proposed Solution

Include compact count in the statusline JSON input:

{
"session_id": "...",
"session_compact_count": 2,
"context_window": { ... }
}

This would be consistent with how context_window.current_usage is already provided, and eliminates the race condition since data comes from the same source.

Alternative Solutions

_No response_

Priority

Medium - Would be very helpful

Feature Category

CLI commands and flags

Use Case Example

Displaying compact count in the statusline (e.g., ⚡⚡ for 2 compacts) helps users understand:

• How long/complex their session has been
• When they're working in a heavily-compacted session where older context may be summarized
• Session health at a glance alongside context usage

Additional Context

Related to https://github.com/anthropics/claude-code/issues/15184 which requests autocompact settings. This request is for compact count - complementary but distinct data.