docs: document delegation width + depth knobs (#13745)

Fills the three gaps left by the orchestrator/width-depth salvage:

- configuration.md §Delegation: max_concurrent_children, max_spawn_depth,
  orchestrator_enabled are now in the canonical config.yaml reference
  with a paragraph covering defaults, clamping, role-degradation, and
  the 3x3x3=27-leaf cost scaling.
- environment-variables.md: adds DELEGATION_MAX_CONCURRENT_CHILDREN to
  the Agent Behavior table.
- features/delegation.md: corrects stale 'default 5, cap 8' wording
  (that was from the original PR; the salvage landed on default 3 with
  no ceiling and a tool error on excess instead of truncation).

website/docs/reference/environment-variables.md

@@ -367,6 +367,7 @@ For cloud sandbox backends, persistence is filesystem-oriented. `TERMINAL_LIFETI
 | `HERMES_ENABLE_PROJECT_PLUGINS` | Enable auto-discovery of repo-local plugins from `./.hermes/plugins/` (`true`/`false`, default: `false`) |
 | `HERMES_BACKGROUND_NOTIFICATIONS` | Background process notification mode in gateway: `all` (default), `result`, `error`, `off` |
 | `HERMES_EPHEMERAL_SYSTEM_PROMPT` | Ephemeral system prompt injected at API-call time (never persisted to sessions) |
+| `DELEGATION_MAX_CONCURRENT_CHILDREN` | Max parallel subagents per `delegate_task` batch (default: `3`, floor of 1, no ceiling). Also configurable via `delegation.max_concurrent_children` in `config.yaml` — the config value takes priority. |
 
 ## Interface
 

website/docs/user-guide/configuration.md

@@ -1332,6 +1332,9 @@ delegation:
   # provider: "openrouter"                  # Override provider (empty = inherit parent)
   # base_url: "http://localhost:1234/v1"    # Direct OpenAI-compatible endpoint (takes precedence over provider)
   # api_key: "local-key"                    # API key for base_url (falls back to OPENAI_API_KEY)
+  max_concurrent_children: 3                # Parallel children per batch (floor 1, no ceiling). Also via DELEGATION_MAX_CONCURRENT_CHILDREN env var.
+  max_spawn_depth: 1                        # Delegation tree depth cap (1-3, clamped). 1 = flat (default): parent spawns leaves that cannot delegate. 2 = orchestrator children can spawn leaf grandchildren. 3 = three levels.
+  orchestrator_enabled: true                # Global kill switch. When false, role="orchestrator" is ignored and every child is forced to leaf regardless of max_spawn_depth.
 ```
 
 **Subagent provider:model override:** By default, subagents inherit the parent agent's provider and model. Set `delegation.provider` and `delegation.model` to route subagents to a different provider:model pair — e.g., use a cheap/fast model for narrowly-scoped subtasks while your primary agent runs an expensive reasoning model.
@@ -1342,6 +1345,8 @@ The delegation provider uses the same credential resolution as CLI/gateway start
 
 **Precedence:** `delegation.base_url` in config → `delegation.provider` in config → parent provider (inherited). `delegation.model` in config → parent model (inherited). Setting just `model` without `provider` changes only the model name while keeping the parent's credentials (useful for switching models within the same provider like OpenRouter).
 
+**Width and depth:** `max_concurrent_children` caps how many subagents run in parallel per batch (default `3`, floor of 1, no ceiling). Can also be set via the `DELEGATION_MAX_CONCURRENT_CHILDREN` env var. When the model submits a `tasks` array longer than the cap, `delegate_task` returns a tool error explaining the limit rather than silently truncating. `max_spawn_depth` controls the delegation tree depth (clamped to 1-3). At the default `1`, delegation is flat: children cannot spawn grandchildren, and passing `role="orchestrator"` silently degrades to `leaf`. Raise to `2` so orchestrator children can spawn leaf grandchildren; `3` for three-level trees. The agent opts into orchestration per call via `role="orchestrator"`; `orchestrator_enabled: false` forces every child back to leaf regardless. Cost scales multiplicatively — at `max_spawn_depth: 3` with `max_concurrent_children: 3`, the tree can reach 3×3×3 = 27 concurrent leaf agents. See [Subagent Delegation → Depth Limit and Nested Orchestration](features/delegation.md#depth-limit-and-nested-orchestration) for usage patterns.
+
 ## Clarify
 
 Configure the clarification prompt behavior:

website/docs/user-guide/features/delegation.md

@@ -121,7 +121,7 @@ delegate_task(
 
 When you provide a `tasks` array, subagents run in **parallel** using a thread pool:
 
-- **Maximum concurrency:** 5 tasks by default (configurable via `delegation.max_concurrent_children`, absolute cap of 8)
+- **Maximum concurrency:** 3 tasks by default (configurable via `delegation.max_concurrent_children` or the `DELEGATION_MAX_CONCURRENT_CHILDREN` env var; floor of 1, no hard ceiling). Batches larger than the limit return a tool error rather than being silently truncated.
 - **Thread pool:** Uses `ThreadPoolExecutor` with the configured concurrency limit as max workers
 - **Progress display:** In CLI mode, a tree-view shows tool calls from each subagent in real-time with per-task completion lines. In gateway mode, progress is batched and relayed to the parent's progress callback
 - **Result ordering:** Results are sorted by task index to match input order regardless of completion order