feat: contexting status --json for machine-readable project state

[ktappdev]

Problem

External tools (LLM agents, editor extensions, CI scripts) need to discover contexting's file paths and health state for a project. Currently they either:

• Hardcode paths like .ctx/ctx_index.json — breaks when config customizes them
• Shell out to contexting doctor --json — overloaded with health checks, noisy
• Parse .ctx/ctx_config.toml directly — fragile, format may change

The other approach (hardcoding wrong paths like .contexting_runtime.json and context.json) already caused bugs in downstream tools.

Proposed Solution

Add contexting status --json that returns a focused machine-readable object:

{
  "project_root": "/path/to/project",
  "config_path": ".ctx/ctx_config.toml",
  "index_path": ".ctx/ctx_index.json",
  "cache_path": ".ctx/ctx_cache.json",
  "runtime_path": ".ctx/ctx_runtime.json",
  "index_exists": true,
  "index_generated_at": "2026-06-16T10:00:00Z",
  "cache_entries": 42,
  "watch_running": true,
  "watch_pid": 12345,
  "watch_address": "127.0.0.1:54321"
}

Implementation Notes

• Reuse resolveConfigPath for path resolution (same as search-hints/eval)
• Check runtime file existence + PID liveness for watch_running
• ContextIndex.GeneratedAt already exists in .ctx/ctx_index.json
• Cache entry count from len(LoadSynonymCache(...))
• Skip config prompt in PersistentPreRunE (add "status" to skip list)

Acceptance Criteria

• contexting status --json returns valid JSON with all fields above
• Paths respect --config flag and config file values
• watch_running is true only if runtime file exists AND PID is alive
• Works from any subdirectory (resolves config path to absolute)
• No config prompt when config doesn't exist