Make workspace, agent, and schedule automation consistent (#2186)

* feat(workspaces): align agent and schedule automation

Make workspace identity the shared placement boundary for MCP and CLI, while caller identity determines parentage. Keep heartbeats minimal and cron-based without changing legacy rolling interval semantics.

* test(cli): expect canonical schedule cadence

* fix(automation): preserve workspace and schedule compatibility

* fix(automation): preserve compatibility edges

* fix(workspaces): align MCP lifecycle resolution

* fix(workspaces): preserve creation intent

* fix(workspaces): preserve branch and schedule identity

packages/app/src/utils/schedule-format.test.ts

@@ -6,6 +6,7 @@ import {
   formatCadence,
   formatNextRun,
   isNewAgentSchedule,
+  scheduleProductName,
   partsToEveryMs,
   resolveScheduleTitle,
   validateCron,
@@ -54,6 +55,11 @@ describe("schedule title helpers", () => {
     expect(isNewAgentSchedule(createSchedule({ targetType: "agent" }))).toBe(false);
   });
 
+  it("labels engine records by product meaning", () => {
+    expect(scheduleProductName(createSchedule({ targetType: "new-agent" }))).toBe("Schedule");
+    expect(scheduleProductName(createSchedule({ targetType: "agent" }))).toBe("Heartbeat");
+  });
+
   it("resolves display titles by name, config title, prompt, then fallback", () => {
     expect(
       resolveScheduleTitle(createSchedule({ name: "Morning run", title: "Config title" })),