process sidecar: independent process manager for long-running work

Introduces a separate Bun process (port 5100) that owns all spawned
processes and long-running work, so the API server can restart freely
without disrupting active sessions.

The sidecar owns:
- Anthropic proxy (port 5051) with persisted secret across restarts
- Claude Code process spawning and session tracking (--resume support)
- Pi agent spawning and RPC lifecycle (prompt/abort/thinking)
- Job queue engine (lane processing, retries, notifications)

The API server becomes a thin client that forwards commands over a
single WebSocket connection with auto-reconnect. send-claude-code.ts
goes from 550 lines of spawn logic to 73 lines of sidecar delegation.

State persisted to data/sidecar/state.json every 30s and on shutdown.
Lockfile prevents duplicate instances. See SIDECAR.md for full docs
and manual testing procedures.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

ecosystem.config.cjs

@@ -1,5 +1,11 @@
 module.exports = {
   apps: [
+    {
+      name: 'officer-sidecar',
+      script: 'bun',
+      args: 'run src/servers/sidecar/index.ts',
+      watch: false,
+    },
     {
       name: 'officer',
       script: 'bun',