test(desktop): cover a handle left open after Host teardown

Drive the built Host through the update handoff with a handle opened on
shutdown, and state why the exit skips startup failures.

apps/desktop-host/src/index.ts

@@ -55,7 +55,8 @@ async function main(): Promise<void> {
     await running?.shutdown.shutdown(0)
     await send({ type: 'shutdown-complete' })
     if (process.connected) process.disconnect()
-    // The application tree is disposed; a handle it left open must not delay the update handoff deadline.
+    // A handle a disposed plugin left open would otherwise keep the Host alive past the shell's graceful
+    // deadline; a startup failure keeps its own diagnostic exit.
     if (running !== undefined) process.exit()
   })()
   process.on('message', (message: unknown) => {

apps/desktop/tests/welcome-flow.e2e.ts

@@ -184,6 +184,11 @@ describe.skipIf(!existsSync(builtHost))('built Desktop welcome flow', () => {
       await backend!.account.cancel(waiting.attempt!.id)
       expect((await fetch(late, { redirect: 'manual' })).status).not.toBe(302)
       expect(await status()).toMatchObject({ loggedIn: false })
+      // A handle left open after acknowledged teardown must not fail the update handoff.
+      vi.stubEnv('NODE_OPTIONS', `--import=data:text/javascript,${encodeURIComponent(
+        "process.on('message', message => { if (message?.type === 'shutdown') setInterval(() => {}, 1000) })")}`)
+      await restart()
+      await host!.stop(true)
     } finally {
       await host?.stop()
       await platform.close()