Preserve opened subagents when parents are archived (#3279)

* fix(subagents): preserve opened children on parent archive

Opening a managed child represents user ownership only while that client's tab remains open. Track that intent per client, detach surviving children during parent archive, and keep single and bulk tab-close behavior consistent.

* fix(subagents): mark generic tab openings

Centralize managed child tab ownership in agent navigation so list, command-center, deep-link, notification, and subagent-track openings all mark ownership before creating the tab. Use stable localized errors for lifecycle failures.

* fix(subagents): classify cold tab openings

Fetch uncached agents before deciding whether tab ownership must be recorded, so notification, desktop, and cold-route openings cannot bypass parent archive protection.

* fix(app): translate navigation fallback errors

* fix(navigation): allow offline workspace intents

* refactor(app): derive subagent ownership from open tabs

* fix(server): serialize subagent lifecycle ownership

packages/protocol/src/agent-labels.ts

@@ -1,4 +1,13 @@
 export const PARENT_AGENT_ID_LABEL = "paseo.parent-agent-id";
+const OPEN_AGENT_TAB_LABEL_PREFIX = "paseo.open-agent-tab.";
+
+export function getOpenAgentTabLabel(clientId: string): string {
+  return `${OPEN_AGENT_TAB_LABEL_PREFIX}${clientId}`;
+}
+
+export function isOpenAgentTabLabel(label: string): boolean {
+  return label.startsWith(OPEN_AGENT_TAB_LABEL_PREFIX);
+}
 
 export interface AgentLabelSource {
   labels?: Record<string, unknown> | null;
@@ -14,3 +23,9 @@ export function getParentAgentIdFromLabels(labels: Record<string, unknown> | nul
 export function isDelegatedAgent(agent: AgentLabelSource): boolean {
   return getParentAgentIdFromLabels(agent.labels) !== null;
 }
+
+export function hasOpenAgentTab(labels: Record<string, unknown> | null | undefined): boolean {
+  return Object.entries(labels ?? {}).some(
+    ([label, value]) => isOpenAgentTabLabel(label) && value === "true",
+  );
+}