feat(notifications): add notifySubagents toggle to suppress subagent turn pings

A parent agent that spawns 8 subagents was producing 9 "Turn complete"
notifications per round — almost always noise. New `notifySubagents`
config flag (defaults to false) gates `turn-completed` and `turn-error`
from any tab with a `parentTabId`. The flag is intentionally NOT applied
to `permission-required` — a subagent's permission prompt still needs a
human tap to proceed, so suppressing it would silently hang the
subagent. `agent-spawned` is already top-level-only by construction.

Wiring:
- core/notifications/types.ts: NtfyConfig.notifySubagents: boolean
- core/notifications/config.ts: defaults to false; normalize() tolerates
  missing / wrong-typed values and falls back to false
- core/notifications/dispatcher.ts: new optional TabParentLookup option
  (getTabParentId). When notifySubagents=false AND the lookup returns a
  non-empty parent id string, turn-completed/turn-error are dropped.
  Lookup failures (no lookup configured, throws, returns undefined) fall
  back to "treat as top-level" so legitimate top-level events are never
  silently dropped when the DB is briefly unreadable.
- api/app.ts: wires getTabParentId via core's getTab(id)?.parentTabId
- frontend SettingsPanel.svelte: "Include subagent tabs" checkbox with
  an explanatory hint that permission prompts still fire

Tests (+9):
- 3 in config.test.ts: default-false, explicit-true, wrong-typed fallback
- 6 in dispatcher.test.ts: suppression of turn-completed/turn-error from
  subagents, no suppression when flag is true, permission-required not
  gated, graceful fallback when lookup is missing/throws/returns undefined

Live ntfy.sh round-trip re-verified (status: 200).

4 files changed, 61 insertions, 0 deletions

diff --git a/packages/core/src/notifications/config.ts b/packages/core/src/notifications/config.ts
index 310c606..faa316e 100644
--- a/packages/core/src/notifications/config.ts
+++ b/packages/core/src/notifications/config.ts
@@ -17,6 +17,7 @@ export function defaultNtfyConfig(): NtfyConfig {
 		topicUrl: "",
 		authToken: "",
 		events: { ...NTFY_DEFAULT_EVENTS },
+		notifySubagents: false,
 	};
 }
 
@@ -34,6 +35,8 @@ export function normalizeNtfyConfig(raw: unknown): NtfyConfig {
 		topicUrl: typeof obj.topicUrl === "string" ? obj.topicUrl : base.topicUrl,
 		authToken: typeof obj.authToken === "string" ? obj.authToken : base.authToken,
 		events: { ...base.events },
+		notifySubagents:
+			typeof obj.notifySubagents === "boolean" ? obj.notifySubagents : base.notifySubagents,
 	};
 	const rawEvents = obj.events;
 	if (rawEvents && typeof rawEvents === "object") {
diff --git a/packages/core/src/notifications/dispatcher.ts b/packages/core/src/notifications/dispatcher.ts
index 4f4fc79..01ce00c 100644
--- a/packages/core/src/notifications/dispatcher.ts
+++ b/packages/core/src/notifications/dispatcher.ts
@@ -31,6 +31,15 @@ export interface PermissionPromptSource {
 /** Look up a human-readable tab title for nicer notification text. */
 export type TabTitleLookup = (tabId: string) => string | null;
 
+/**
+ * Look up a tab's `parentTabId`. Returns `null` for top-level tabs (no
+ * parent) and `undefined` when the lookup can't be performed (no DB, tab
+ * not found). Both non-strings cause the dispatcher to fall back to
+ * "treat as top-level" to avoid silently dropping notifications when the
+ * lookup is broken.
+ */
+export type TabParentLookup = (tabId: string) => string | null | undefined;
+
 export interface DispatcherOptions {
 	/** Override the config loader (tests). Defaults to `loadNtfyConfig`. */
 	loadConfig?: () => NtfyConfig;
@@ -41,6 +50,13 @@ export interface DispatcherOptions {
 	/** Look up a tab title for richer titles. */
 	getTabTitle?: TabTitleLookup;
 	/**
+	 * Look up a tab's `parentTabId`. Used to honour the
+	 * `notifySubagents` config flag — when false, `turn-completed` /
+	 * `turn-error` from subagent tabs (those with a parent) are
+	 * suppressed.
+	 */
+	getTabParentId?: TabParentLookup;
+	/**
 	 * How long (ms) a dedupeKey is suppressed for. Permission prompts re-emit
 	 * the whole pending list on every change, so dedupe is essential.
 	 */
@@ -51,6 +67,7 @@ export class NotificationDispatcher {
 	private loadConfig: () => NtfyConfig;
 	private send: (config: NtfyConfig, event: NotificationEvent) => Promise<unknown>;
 	private getTabTitle: TabTitleLookup | undefined;
+	private getTabParentId: TabParentLookup | undefined;
 	private dedupeWindowMs: number;
 	/** Recently-sent dedupeKey → expiresAt epoch ms. */
 	private recentlySent = new Map<string, number>();
@@ -61,6 +78,7 @@ export class NotificationDispatcher {
 		this.send =
 			opts.send ?? ((config, event) => sendNtfy(config, event, opts.fetchImpl ?? undefined));
 		this.getTabTitle = opts.getTabTitle;
+		this.getTabParentId = opts.getTabParentId;
 		this.dedupeWindowMs = opts.dedupeWindowMs ?? 5_000;
 	}
 
@@ -101,12 +119,22 @@ export class NotificationDispatcher {
 	 *
 	 * `status` events are ignored — they fire on every transition and we'd
 	 * either spam or duplicate the `done`/`error` notifications.
+	 *
+	 * Turn events from subagent tabs are suppressed when
+	 * `config.notifySubagents === false` (the default). A parent agent
+	 * spawning 8 subagents would otherwise produce 9 "Turn complete"
+	 * pushes per round; almost always noise. Permission prompts are NOT
+	 * gated this way — a subagent's permission request still needs human
+	 * input to proceed, so suppressing those would silently hang the
+	 * subagent.
 	 */
 	attachToAgentManager(source: AgentEventSource): () => void {
 		const unsub = source.onEvent((event) => {
 			if (event.type === "done") {
+				if (this.isSubagentSuppressed(event.tabId)) return;
 				this.notify(this.buildTurnCompleted(event));
 			} else if (event.type === "error") {
+				if (this.isSubagentSuppressed(event.tabId)) return;
 				this.notify(this.buildTurnError(event));
 			} else if (event.type === "tab-created") {
 				const ev = event as unknown as {
@@ -213,6 +241,27 @@ export class NotificationDispatcher {
 		return `tab ${tabId.slice(0, 8)}`;
 	}
 
+	/**
+	 * Returns true when this `tabId` belongs to a subagent AND the user has
+	 * opted out of subagent turn notifications. On lookup failure
+	 * (`getTabParentId` returns `undefined` or throws) we err on the side
+	 * of "not a subagent" — better to over-notify than to silently drop
+	 * legitimate top-level events when the DB is briefly unreadable.
+	 */
+	private isSubagentSuppressed(tabId: string): boolean {
+		const config = this.loadConfig();
+		if (config.notifySubagents) return false;
+		if (!this.getTabParentId) return false;
+		let parent: string | null | undefined;
+		try {
+			parent = this.getTabParentId(tabId);
+		} catch {
+			return false;
+		}
+		// Only a non-empty string parent id means "this tab is a subagent".
+		return typeof parent === "string" && parent.length > 0;
+	}
+
 	// ─── Dedupe helpers ───────────────────────────────────────────
 
 	private isDuplicate(key: string): boolean {
diff --git a/packages/core/src/notifications/index.ts b/packages/core/src/notifications/index.ts
index ea99a58..d9d934d 100644
--- a/packages/core/src/notifications/index.ts
+++ b/packages/core/src/notifications/index.ts
@@ -14,6 +14,7 @@ export {
 	type DispatcherOptions,
 	NotificationDispatcher,
 	type PermissionPromptSource,
+	type TabParentLookup,
 	type TabTitleLookup,
 } from "./dispatcher.js";
 export { type FetchLike, type NtfySendResult, sendNtfy, validateTopicUrl } from "./ntfy.js";
diff --git a/packages/core/src/notifications/types.ts b/packages/core/src/notifications/types.ts
index f6baa27..238cb68 100644
--- a/packages/core/src/notifications/types.ts
+++ b/packages/core/src/notifications/types.ts
@@ -57,12 +57,20 @@ export interface NotificationEvent {
  * - `authToken` — optional bearer token for private ntfy servers.
  * - `events` — per-event-type enable map. Missing entries default to OFF
  *   so a newly-added event type doesn't silently start firing.
+ * - `notifySubagents` — when false (default), `turn-completed` and
+ *   `turn-error` notifications from subagent tabs (tabs with a
+ *   `parentTabId`) are suppressed. A parent agent that spawns 8
+ *   subagents would otherwise push 9 "Turn complete" notifications per
+ *   round — usually noise. `permission-required` is NOT gated: even a
+ *   subagent's permission prompt needs a human tap to proceed.
+ *   `agent-spawned` is already top-level-only by construction.
  */
 export interface NtfyConfig {
 	enabled: boolean;
 	topicUrl: string;
 	authToken: string;
 	events: Record<NotificationEventType, boolean>;
+	notifySubagents: boolean;
 }
 
 /** All event types this build knows about (the source of truth for UI). */