fix: scope sidecar exit handling to the active process

Wait for an intentional sidecar dispose to exit before refreshing capabilities, and ignore exit events from stale sidecar processes. This prevents a refresh from killing the old process and then having that old exit reject the new capabilities request with an unexpected sidecar exit error.

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

tests/main/sidecarRefresh.test.ts

@@ -1,6 +1,9 @@
 import { describe, expect, test } from 'bun:test';
 
-import { shouldRestartSidecarOnCapabilityRefresh } from '@main/sidecar/sidecarRefresh';
+import {
+  shouldHandleSidecarExit,
+  shouldRestartSidecarOnCapabilityRefresh,
+} from '@main/sidecar/sidecarRefresh';
 
 describe('shouldRestartSidecarOnCapabilityRefresh', () => {
   test('restarts the sidecar when no run-turn is active', () => {
@@ -11,3 +14,18 @@ describe('shouldRestartSidecarOnCapabilityRefresh', () => {
     expect(shouldRestartSidecarOnCapabilityRefresh(true)).toBe(false);
   });
 });
+
+describe('shouldHandleSidecarExit', () => {
+  test('handles exit events from the currently active sidecar process', () => {
+    expect(shouldHandleSidecarExit(1234, 1234)).toBe(true);
+  });
+
+  test('ignores exit events from a stale sidecar process', () => {
+    expect(shouldHandleSidecarExit(1234, 5678)).toBe(false);
+  });
+
+  test('ignores exit events when either process id is missing', () => {
+    expect(shouldHandleSidecarExit(undefined, 5678)).toBe(false);
+    expect(shouldHandleSidecarExit(1234, undefined)).toBe(false);
+  });
+});