refactor: generalize background execution contract

packages/core/src/scheduler/tool-executor.test.ts

@@ -469,7 +469,7 @@ describe('ToolExecutor', () => {
     expect(result.status).toBe(CoreToolCallStatus.Success);
   });
 
-  it('should report PID updates for shell tools', async () => {
+  it('should report execution ID updates for backgroundable tools', async () => {
     // 1. Setup ShellToolInvocation
     const messageBus = createMockMessageBus();
     const shellInvocation = new ShellToolInvocation(
@@ -480,7 +480,7 @@ describe('ToolExecutor', () => {
     // We need a dummy tool that matches the invocation just for structure
     const mockTool = new MockTool({ name: SHELL_TOOL_NAME });
 
-    // 2. Mock executeToolWithHooks to trigger the PID callback
+    // 2. Mock executeToolWithHooks to trigger the execution ID callback
     const testPid = 12345;
     vi.mocked(coreToolHookTriggers.executeToolWithHooks).mockImplementation(
       async (
@@ -490,13 +490,13 @@ describe('ToolExecutor', () => {
         _tool,
         _liveCb,
         _shellCfg,
-        setPidCallback,
+        setExecutionIdCallback,
         _config,
         _originalRequestName,
       ) => {
-        // Simulate the shell tool reporting a PID
-        if (setPidCallback) {
-          setPidCallback(testPid);
+        // Simulate the tool reporting an execution ID
+        if (setExecutionIdCallback) {
+          setExecutionIdCallback(testPid);
         }
         return { llmContent: 'done', returnDisplay: 'done' };
       },
@@ -525,7 +525,7 @@ describe('ToolExecutor', () => {
       onUpdateToolCall,
     });
 
-    // 4. Verify PID was reported
+    // 4. Verify execution ID was reported
     expect(onUpdateToolCall).toHaveBeenCalledWith(
       expect.objectContaining({
         status: CoreToolCallStatus.Executing,