Invite a friend; handle field shows the domain; system mail fixes

- Invitations: each user can invite two friends by email (sign-up works
  through the link even while registration is closed); admin-editable
  template, subject and sender.
- Invitation sender defaults to the system-mail From address, which the
  SMTP account is allowed to send as (was postmaster@APP_DOMAIN, refused
  with 553 when the two differ).
- Sign-in, sign-up and forgot-password fields show the fixed
  @domain after the typed name; the registration status reports it.
- System mail gets a Date header; the invitation's plain-text part keeps
  its paragraphs and line breaks.
- SMTP EHLO uses SMTP_HELO_NAME / APP_DOMAIN, not the container name.
- DNS recommendations for the mail domains.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

backend/app/identity/routes.py

@@ -18,7 +18,7 @@ from app.config import get_settings
 from app.db import get_session
 from app.events import get_event_bus
 from app.hosted.admin import MailServerError
-from app.identity import app_passwords, trusted_devices
+from app.identity import app_passwords, invitations, trusted_devices
 from app.identity import totp as totp_mod
 from app.identity.cookies import (
     clear_auth_cookies,
@@ -40,6 +40,8 @@ from app.identity.schemas import (
     AppPasswordCreatedOut,
     AppPasswordIn,
     AppPasswordOut,
+    InvitationCheckIn,
+    InvitationCheckOut,
     LoginRequest,
     MessageOut,
     PasswordResetCheckIn,
@@ -116,12 +118,31 @@ def _user_out(user: User) -> UserOut:
 async def registration(db: DbSession) -> RegistrationStatusOut:
     """Whether signup is open. Unauthenticated: the signup page needs it to render."""
     status = await registration_status(db)
-    return RegistrationStatusOut(open=status.open, bootstrap=status.bootstrap)
+    return RegistrationStatusOut(
+        open=status.open, bootstrap=status.bootstrap, domain=get_settings().app_domain
+    )
 
 
 _REGISTRATION_ERROR_STATUS = {"handle_taken": 409, "registration_closed": 403}
 
 
+@router.post("/invitation/check", response_model=InvitationCheckOut)
+async def invitation_check(body: InvitationCheckIn, db: DbSession) -> InvitationCheckOut:
+    """Whether an invitation link still works, and who it is from — for the
+    sign-up page. Does not use it up."""
+    if not (await app_settings(db)).invitations_enabled:
+        return InvitationCheckOut(valid=False)
+    invitation = await invitations.find_valid(db, body.token)
+    if invitation is None:
+        return InvitationCheckOut(valid=False)
+    inviter = await db.get(User, invitation.inviter_id)
+    return InvitationCheckOut(
+        valid=True,
+        invitee_name=invitation.invitee_name,
+        inviter_name=await invitations.inviter_name(db, inviter) if inviter else "",
+    )
+
+
 @router.post("/register", response_model=UserOut)
 async def register(
     body: RegisterRequest, request: Request, response: Response, db: DbSession
@@ -130,15 +151,28 @@ async def register(
         await check_new_password(body.password, resolve_handle(body.localpart))
     except PasswordRejected as exc:
         raise_api_error(400, exc.code, exc.message)
+    invitation_id: uuid.UUID | None = None
+    if body.invite:
+        # Used up in this same transaction: if the sign-up fails (the address
+        # is taken, …) the rollback hands the invitation back.
+        if (await app_settings(db)).invitations_enabled:
+            invitation_id = await invitations.claim(db, body.invite)
+        if invitation_id is None:
+            raise_api_error(
+                400, "invalid_invitation", "this invitation has already been used or has expired"
+            )
     try:
         user = await register_user(
             db,
             localpart=body.localpart,
             password=body.password,
             recovery_email=body.recovery_email,
+            invited=invitation_id is not None,
         )
     except RegistrationError as exc:
         raise_api_error(_REGISTRATION_ERROR_STATUS.get(exc.code, 400), exc.code, exc.message)
+    if invitation_id is not None:
+        await invitations.record_user(db, invitation_id, user.id)
     await db.commit()
     # The user's own mailbox (App. D §D.4): it exists on the mail server as soon
     # as the user does (the directory reads the users table); this adds it to