chat: persistent Agent SDK session per chat — decouple worker from turn (Phase 1)

Root fix for orphaned background tasks: the platform drove Claude Code as a
one-shot `claude -p` per turn (stdin ignored, process exits at turn end), so
run_in_background/Monitor work — and its task_notification — had no live harness
to return to. Now each chat session runs ONE long-lived Agent SDK query() with
streaming input; turns are user messages pushed onto it, and the session stays
warm between turns.

- claude-manager: persistent `query({ prompt: AsyncIterable, options })` per
  sessionKey (bypassPermissions, --resume, mcp via extraArgs, CLAUDECODE stripped).
  Single consumer loop maps every SDK message → ChatEvent, incl. post-turn
  task_started / task_notification. interrupt() = stop-turn; abort() = kill-session;
  30-min idle GC.
- stream-parser: processMessage() (object-level, reused by the SDK loop) + task
  message handling. ChatEvent/ServerMessage gain task:started / task:notification.
- API: the sidecar event subscription is now SESSION-scoped (no longer unsubscribes
  on 'result'), so background events after turn-end still reach the client. First
  turn opens the session; later turns push onto it. handleStop → interrupt (keeps
  session warm); disconnect/deleteSession → kill.
- protocol/sidecar-registry/user-instance: claude:interrupt command + interruptClaude.
- client: render task:started / task:notification in the transcript.

Verified end-to-end through the real chat WS: a run_in_background task's completion
arrives ~6s AFTER the turn's result; multi-turn on one warm session works.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

src/servers/sidecar/protocol.ts

@@ -15,6 +15,7 @@ export type SidecarCommand =
   | { type: 'claude:spawn'; id: string; params: ClaudeSpawnParams }
   | { type: 'claude:spawn-streaming'; id: string; params: ClaudeSpawnStreamingParams }
   | { type: 'claude:kill'; id: string; sessionKey: string }
+  | { type: 'claude:interrupt'; id: string; sessionKey: string }
   | { type: 'claude:clear-session'; id: string; sessionKey: string }
   // OpenCode — drive a turn via `opencode run … --format json` (tools re-anchored to cwd via --dir)
   | { type: 'opencode:run-streaming'; id: string; params: OpenCodeRunParams }
@@ -38,6 +39,7 @@ export type SidecarEvent =
   | { type: 'claude:result'; id: string; result: ClaudeCodeResult }
   | { type: 'claude:error'; id: string; error: string }
   | { type: 'claude:killed'; id: string }
+  | { type: 'claude:interrupted'; id: string }
   | { type: 'claude:session-cleared'; id: string }
   // VNC
   | { type: 'vnc:started'; id: string; port: number; display: number }