fix(profile): no Add GitHub where people sign in with a password

Someone identified was offered Add GitHub wherever GitHub signed people in,
and on an instance offering passwords the browser round trip ended in
"Couldn't sign in with GitHub.", as the instance adds GitHub to nobody there
(ADR 0017, D2; the end-to-end test of 21 Oct). The profile now shows the
GitHub row there only to whom it signs in already, and an anonymous
person's Sign in with GitHub, which still reaches the account someone has,
says why it didn't: a GitHub account nobody has, with the password beneath
in its place, or one that signs in with its password now.

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/github_sign_in_test.dart

@@ -206,4 +206,97 @@ void main() {
     expect(find.text('Switch to your GitHub account?'), findsNothing);
     expect(find.byType(HomeScreen), findsOneWidget);
   });
+
+  group('where people sign in with a password (ADR 0017)', () {
+    setUp(() => auth.linksGitHub = false);
+
+    testWidgets('anonymous people may still sign in with the GitHub account '
+        'they have; one nobody has is said so, with the password in its '
+        'place', (tester) async {
+      await openProfile(tester);
+      expect(find.text('Sign in with GitHub'), findsOneWidget);
+
+      auth.gitHubError = const GitHubSignInFailed(
+        GitHubSignInProblem.deprecated,
+      );
+      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. To keep '
+          'your progress, set up a password instead.',
+        ),
+        findsOneWidget,
+      );
+      expect(find.text("Couldn't sign in with GitHub."), findsNothing);
+      expect(
+        find.text('Progress is saved on this device. Sign in to keep it.'),
+        findsOneWidget,
+      );
+    });
+
+    testWidgets('a GitHub account that signs in with its password now is '
+        'said so', (tester) async {
+      auth
+        ..gitHubLinkOutcome = GitHubLinkOutcome.takenByAnotherPerson
+        ..gitHubSwitchError = const GitHubSignInFailed(
+          GitHubSignInProblem.usePassword,
+        );
+      await openProfile(tester);
+
+      await tester.tap(find.text('Sign in with GitHub'));
+      await tester.pumpAndSettle();
+
+      expect(
+        find.text(
+          'This account signs in with its email address and password now, '
+          'not with GitHub.',
+        ),
+        findsOneWidget,
+      );
+      expect(auth.gitHubSwitches, 0);
+    });
+  });
+
+  group('someone identified', () {
+    setUp(() {
+      auth = FakeAuthGateway(
+        status: const SignedIn(authUserId: 'ada', isIdentified: true),
+      );
+      auth.addressOwners['ada@example.org'] = 'ada';
+    });
+
+    testWidgets('is offered to add GitHub where the instance adds it', (
+      tester,
+    ) async {
+      await openProfile(tester);
+
+      expect(find.text('Add GitHub'), findsOneWidget);
+    });
+
+    testWidgets('is offered no GitHub to add where people sign in with a '
+        'password (ADR 0017): the instance would refuse it', (tester) async {
+      auth.linksGitHub = false;
+
+      await openProfile(tester);
+
+      expect(find.text('Add GitHub'), findsNothing);
+      expect(find.text('GitHub'), findsNothing);
+      expect(find.text('Email address'), findsOneWidget);
+    });
+
+    testWidgets('who has GitHub there sees it signs them in, with nothing to '
+        'add', (tester) async {
+      auth
+        ..linksGitHub = false
+        ..gitHubPeople.add('ada');
+
+      await openProfile(tester);
+
+      expect(find.text('GitHub'), findsOneWidget);
+      expect(find.text('Signs you in'), findsWidgets);
+      expect(find.text('Add GitHub'), findsNothing);
+    });
+  });
 }