refactor(halkyon_app): the app says where GitHub is added later

The start screen's sentence after a GitHub account nobody here signs in
with named Learn's Profile screen. The package now says only that no
account signs in with it; the app's frame adds the rest as a sentence
of its own (thenAddGitHub), since the place takes its language's
grammar ("im Profil"). Learn's reads as before, which a test now pins.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Signed-off-by: Tizian 「ティツィアーン」 <raisondetredev@pm.me>

apps/learn/halkyon_learn_flutter/test/feature/auth/widget/session_widgets_test.dart

@@ -152,6 +152,30 @@ void main() {
     expect(gateway.signIns, 1);
   });
 
+  testWidgets('from there, a GitHub account nobody here signs in with is said '
+      'so, with where Learn adds GitHub', (tester) async {
+    await openSettings(tester);
+    await tester.tap(find.text('Sign out'));
+    await tester.pumpAndSettle();
+    await tester.tap(find.text('Sign out').last);
+    await tester.pumpAndSettle();
+
+    gateway.gitHubError = const GitHubSignInFailed(
+      GitHubSignInProblem.unknownAccount,
+    );
+    await tester.tap(find.text('Sign in with GitHub'));
+    await tester.pumpAndSettle();
+
+    expect(
+      find.text(
+        'No account here signs in with this GitHub account yet. Start '
+        'without an account, then add GitHub in Profile.',
+      ),
+      findsOneWidget,
+    );
+    expect(gateway.status, const SignedOut());
+  });
+
   testWidgets('from there, an email address starts without an account and '
       'asks for the address on Profile', (tester) async {
     await openSettings(tester);