feat: add AI-powered idle check for respawn controller

Replace the "Worked for Xm Xs" pattern as the sole primary idle
detection signal with a final AI-powered check. When pre-filter
conditions are met (output silence, no working patterns, tokens
stable), a fresh Claude CLI session is spawned in a screen to
analyze terminal output and provide a definitive IDLE/WORKING
verdict before proceeding with the respawn cycle.

New state in state machine: `ai_checking` (between pre-filter
confirmation and `sending_update`). WORKING verdict triggers a
3-minute cooldown. Errors auto-disable after 3 consecutive
failures, falling back to the existing noOutputTimeoutMs safety net.

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

src/types.ts

@@ -211,6 +211,16 @@ export interface RespawnConfig {
   autoAcceptPrompts?: boolean;
   /** Delay before auto-accepting plan mode prompts when no output and no completion message (ms) */
   autoAcceptDelayMs?: number;
+  /** Whether AI idle check is enabled */
+  aiIdleCheckEnabled?: boolean;
+  /** Model to use for AI idle check */
+  aiIdleCheckModel?: string;
+  /** Maximum characters of terminal buffer for AI check */
+  aiIdleCheckMaxContext?: number;
+  /** Timeout for AI check in ms */
+  aiIdleCheckTimeoutMs?: number;
+  /** Cooldown after WORKING verdict in ms */
+  aiIdleCheckCooldownMs?: number;
 }
 
 /**
@@ -515,6 +525,16 @@ export interface PersistedRespawnConfig {
   autoAcceptPrompts?: boolean;
   /** Delay before auto-accepting prompts (ms) */
   autoAcceptDelayMs?: number;
+  /** Whether AI idle check is enabled */
+  aiIdleCheckEnabled?: boolean;
+  /** Model to use for AI idle check */
+  aiIdleCheckModel?: string;
+  /** Maximum characters of terminal buffer for AI check */
+  aiIdleCheckMaxContext?: number;
+  /** Timeout for AI check in ms */
+  aiIdleCheckTimeoutMs?: number;
+  /** Cooldown after WORKING verdict in ms */
+  aiIdleCheckCooldownMs?: number;
   /** Duration in minutes if timed respawn was set */
   durationMinutes?: number;
 }