Replace the default counter widget test with a real smoke test

**Problem**

The only test in the repo is the untouched `flutter create` counter stub. It asserts a counter increments, which this app has never done, so **`flutter test` is red today** and no test gate can be added until it is dealt with.

Fixing the assertion alone does not make it green. Two further failures survive:

- The splash screen schedules a 2-second `Timer` that is never cancelled, because its `State` has no `dispose()`. That trips the pending-timer assertion at teardown.
- The splash screen constructs `AuthService()`, whose private constructor calls `initState()` **without awaiting**, reaching `Hive.initFlutter()`. Under `flutter_test` that throws `MissingPluginException` and surfaces as an unhandled async error.

**Where**

- `test/widget_test.dart:19` asserts `find.text('0')`, but `lib/main.dart:41` sets `initialRoute: '/'` and `lib/services/routing/placement_routes.dart:15-16` maps `/` to `SplashPage`, which renders a logo, "Placement Online", a spinner and a credit line. There is no `'0'`, and the only icon is `Icons.favorite`, so the `find.byIcon(Icons.add)` tap at `:23` is never reached.
- `lib/screens/splash/splash.dart:23` (uncancelled Timer), `:22` (`AuthService()`)
- `lib/services/auth/auth_service.dart:93` (`Hive.initFlutter()`)

**Expected**

`flutter test` passes and asserts something true about this app.

**Fix sketch**

- Delete the stub.
- Add one test that pumps `MyApp()` and asserts the splash screen renders its title, using `pumpAndSettle` and a `path_provider` channel mock.
- Cancel the Timer in a `dispose()` override. That is a prerequisite here and worth doing on its own merits.

**Verification**

Make the new assertion false and confirm `flutter test` fails; restore it and confirm it passes with no pending-timer warning.

Start with test/widget_test.dart and run flutter test to reproduce the counter-stub, pending-timer, and plugin failures. Read lib/main.dart, lib/services/routing/placement_routes.dart, lib/screens/splash/splash.dart, and lib/services/auth/auth_service.dart. Replace the stub with a splash-title smoke test using the path_provider channel mock, cancel the splash Timer on disposal, and verify flutter test passes without pending-timer warnings.

Written by the indexing model from the issue text.