fix(session): persist the delegation depth in the session header

A subagent child's recursion depth lived only in runtime AgentOptions,
so a persisted child came back from resume counted as top-level and
maxDepth stopped binding after every restart. Add
SessionHeader.delegationDepth, round-trip it through the JSONL and
SQLite backends (SQLite schema v5), restore it on agent-loop resume,
and write it when the in-process backends create a child. The seam now
owns the shared depth vocabulary (delegationDepthOf): the persisted
header is authoritative and monotone — runtime options may deepen it
but never lower it.

packages/core/session/src/index.ts

@@ -128,6 +128,10 @@ function snapshotSessionHeader(id: SessionId, source?: SessionHeader): SessionHe
     && (typeof record.seedLength !== 'number' || !Number.isSafeInteger(record.seedLength) || record.seedLength < 0)) {
     throw new Error('session header seedLength must be a non-negative safe integer')
   }
+  if (record.delegationDepth !== undefined
+    && (typeof record.delegationDepth !== 'number' || !Number.isSafeInteger(record.delegationDepth) || record.delegationDepth < 0)) {
+    throw new Error('session header delegationDepth must be a non-negative safe integer')
+  }
   return deepFreeze(record as unknown as SessionHeader)
 }
 
@@ -650,6 +654,7 @@ export class SessionStore extends Service {
       ...meta?.cwd === undefined ? {} : { cwd: meta.cwd },
       ...meta?.parentSession === undefined ? {} : { parentSession: meta.parentSession },
       ...meta?.seedLength === undefined ? {} : { seedLength: meta.seedLength },
+      ...meta?.delegationDepth === undefined ? {} : { delegationDepth: meta.delegationDepth },
     }
     return new Session(sessionId, seed, header)
   }

packages/core/session/src/types.ts

@@ -50,6 +50,12 @@ export interface SessionHeader {
    * boundary lets resume and replay distinguish parent history from child work.
    */
   readonly seedLength?: number
+  /**
+   * Delegation depth: absent (zero) for a top-level session, parent depth + 1
+   * for a subagent child. Persisted so a recursion budget survives restart and
+   * resume — a runtime-only depth would reset a resumed child to top-level.
+   */
+  readonly delegationDepth?: number
 }
 
 /**
@@ -69,6 +75,7 @@ export interface CreateSessionOptions {
     readonly parentSession?: SessionId
     readonly createdAt?: number
     readonly seedLength?: number
+    readonly delegationDepth?: number
   }
 }