fix(app): GitHub's refusals say why, and no hint adds GitHub where passwords are offered

Where an instance offers password sign-in, GitHub is added to nobody (ADR
0017, D2), yet the start screen still said "then add GitHub" after a GitHub
account nobody has, and every refusal but an unknown account read
"Couldn't sign in with GitHub." (the end-to-end test of 21 Oct).

- The gateway tells from one read of the basics whether GitHub signs in and
  whether it is added to people (`gitHubOffer`, in place of
  `gitHubClientId`); the GitHub bloc keeps it (`Ready.linking`) for the
  profile, with why an attempt failed (`Ready.problem`).
- The instance's `usePassword`, `deprecated` and `ended` become problems of
  their own (`gitHubSignInProblemOf`), worded by `gitHubProblemText` and on
  the start screen; an anonymous person refused a link is told the GitHub
  account is nobody's and offered the password instead.
- Where passwords are offered, the start screen offers an account to create
  in place of the app's hint on adding GitHub.

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

@@ -15,13 +15,23 @@ void main() {
   /// The home tab.
   final home = find.byType(HomeScreen);
 
-  Future<void> showApp(WidgetTester tester) =>
-      pumpApp(tester, testDependencies(authGateway: gateway));
+  /// Shows the app, on an instance offering passwords unless [passwords] is
+  /// false.
+  Future<void> showApp(WidgetTester tester, {bool passwords = true}) => pumpApp(
+    tester,
+    testDependencies(
+      authGateway: gateway,
+      passwordGateway: FakePasswordGateway(gateway)..offered = passwords,
+    ),
+  );
 
   /// Shows the app and opens settings, from the profile tab, down to the
   /// account.
-  Future<void> openSettings(WidgetTester tester) async {
-    await showApp(tester);
+  Future<void> openSettings(
+    WidgetTester tester, {
+    bool passwords = true,
+  }) async {
+    await showApp(tester, passwords: passwords);
     await openTab(tester, 'Profile');
     await tester.tap(find.byTooltip('Settings'));
     await tester.pumpAndSettle();
@@ -156,7 +166,8 @@ void main() {
   });
 
   testWidgets('from there, a GitHub account nobody here signs in with is said '
-      'so, with where Learn adds GitHub', (tester) async {
+      'so, with an account to create in its place where passwords are '
+      'offered (ADR 0017)', (tester) async {
     await openSettings(tester);
     await tester.tap(find.text('Sign out'));
     await tester.pumpAndSettle();
@@ -169,6 +180,31 @@ void main() {
     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. Create an '
+        'account with your email address and a password instead.',
+      ),
+      findsOneWidget,
+    );
+    expect(gateway.status, const SignedOut());
+  });
+
+  testWidgets('where no passwords are offered, with where Learn adds GitHub', (
+    tester,
+  ) async {
+    await openSettings(tester, passwords: false);
+    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 '
@@ -176,7 +212,6 @@ void main() {
       ),
       findsOneWidget,
     );
-    expect(gateway.status, const SignedOut());
   });
 
   testWidgets('deleting the account asks first; Cancel keeps it', (