fix(auth)!: a first password takes a fresh proof of the account's way in

The fourth reading's first finding: password.set took a session alone,
so whoever took one made a GitHub-only account, or an address account
without a password, theirs for good (their address or password, their
authenticator; GitHub then refused the owner).

- An account with an address proves it anew: a code mailed to that
  address for this (EmailCodePurpose.firstPassword, its own mail), never
  the session alone, a code asked for anything else, or another address.
- An account that signs in with GitHub alone does it within 10 minutes of
  a GitHub sign-in (the session's method and creation time, where the
  session lives; members tell the register), refused signInAgain before
  any code is used; the address it adds is proved as before.
- Anonymous people still become identified with a code to the address
  they add.

The app mails the code to the person's own address (asking for it where
the device doesn't know it), offers a password right after a GitHub
sign-in (D2's "at their next sign-in") before the person's app, and asks
for a GitHub sign-in anew when the instance refuses an older one, keeping
the code typed.

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

packages/halkyon_app/test/password/bloc/account_setup_cubit_test.dart

@@ -210,6 +210,69 @@ void main() {
     expect((auth.status as SignedIn).authUserId, person);
   });
 
+  test('gives a signed-in person with an address their first password only '
+      'with a code mailed to that address for it, never with the session '
+      'alone (the fourth reading)', () async {
+    await auth.signInAnonymously();
+    final person = (auth.status as SignedIn).authUserId;
+    final first = setUpAs(AccountSetupMode.setPassword)
+      ..addressEntered('anna@example.org');
+    await first.passwordEntered('correct horse', 'correct horse');
+    first.phraseWrittenDown();
+    await first.phraseChecked(wordsAsked(first.state));
+    await first.mailCodeEntered(gateway.codeFor('anna@example.org'));
+    // An address and no password, as codes by mail left accounts.
+    gateway.accountOf(person)
+      ..password = null
+      ..authenticators.clear();
+
+    final cubit = setUpAs(
+      AccountSetupMode.setPassword,
+      address: 'anna@example.org',
+      hasAddress: true,
+    );
+    expect(cubit.state, at(AccountSetupStep.password));
+    await cubit.passwordEntered('another horse', 'another horse');
+    cubit.phraseWrittenDown();
+    await cubit.phraseChecked(wordsAsked(cubit.state));
+
+    expect(cubit.state, at(AccountSetupStep.mailCode));
+    expect(gateway.mailed.last.purpose, MailCodePurpose.firstPassword);
+    await cubit.mailCodeEntered(gateway.codeFor('anna@example.org'));
+    expect(cubit.state, at(AccountSetupStep.authenticator));
+    expect(gateway.accountOf(person).password, 'another horse');
+  });
+
+  test('asks for the address a signed-in person has where the device '
+      "doesn't know it", () {
+    final cubit = setUpAs(AccountSetupMode.setPassword, hasAddress: true);
+    expect(cubit.state, at(AccountSetupStep.address));
+  });
+
+  test('asks GitHub people to sign in with GitHub again where theirs is '
+      'too old, keeping the code for after', () async {
+    await auth.switchToGitHub();
+    gateway
+      ..gitHubPeople.add('github-person')
+      ..staleGitHubSignIns.add('github-person');
+    final cubit = setUpAs(AccountSetupMode.setPassword)
+      ..addressEntered('gina@example.org');
+    await cubit.passwordEntered('correct horse', 'correct horse');
+    cubit.phraseWrittenDown();
+    await cubit.phraseChecked(wordsAsked(cubit.state));
+    final code = gateway.codeFor('gina@example.org');
+
+    await cubit.mailCodeEntered(code);
+    expect(
+      cubit.state,
+      at(AccountSetupStep.mailCode, problem: PasswordProblem.signInAgain),
+    );
+
+    gateway.staleGitHubSignIns.clear();
+    await cubit.mailCodeEntered(code);
+    expect(cubit.state, at(AccountSetupStep.authenticator));
+  });
+
   test("refuses another account's address to a signed-in person, back at "
       'the address', () async {
     gateway.addAccount(