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/schemas.py

@@ -12,6 +12,9 @@ class RegisterRequest(BaseModel):
     localpart: str = Field(min_length=3, max_length=30)
     password: str = Field(min_length=8, max_length=128)
     recovery_email: str | None = None
+    # A friend's invitation (app/identity/invitations.py): signs up even while
+    # public registration is closed, and is used up by it.
+    invite: str | None = Field(default=None, max_length=200)
 
 
 class LoginRequest(BaseModel):
@@ -98,23 +101,39 @@ class UserOut(BaseModel):
     mail_host: str | None = None
 
 
+class InvitationCheckIn(BaseModel):
+    token: str = Field(min_length=1, max_length=200)
+
+
+class InvitationCheckOut(BaseModel):
+    valid: bool
+    invitee_name: str = ""
+    inviter_name: str = ""
+
+
 class RegistrationStatusOut(BaseModel):
     """Public, unauthenticated: what the signup page should show."""
 
     open: bool
     # True when the instance has no users yet, so signup creates the administrator.
     bootstrap: bool
+    # The domain every handle lives under (localpart@domain), shown beside the
+    # handle field.
+    domain: str
 
 
 class AdminSettingsOut(BaseModel):
     registration_open: bool
     default_quota_bytes: int
+    # Users may send friends sign-up invitations (app/identity/invitations.py).
+    invitations_enabled: bool
 
 
 class AdminSettingsIn(BaseModel):
     """Merge semantics: omitted fields are left as they are."""
 
     registration_open: bool | None = None
+    invitations_enabled: bool | None = None
     # Applies to users created after the change; existing mailboxes keep theirs.
     default_quota_bytes: int | None = Field(default=None, gt=0)
 
@@ -145,6 +164,36 @@ class AdminMailIn(BaseModel):
     public_url: str | None = Field(default=None, max_length=500)
 
 
+class AdminInviteTemplateOut(BaseModel):
+    # Empty strings: the built-in subject / template / sender is used.
+    subject: str
+    html: str
+    from_address: str
+    default_subject: str
+    default_html: str
+    default_from: str
+    placeholders: list[str]
+
+
+class AdminInviteTemplateIn(BaseModel):
+    """Merge semantics: omitted fields are left as they are; an empty string
+    goes back to the built-in one."""
+
+    subject: str | None = Field(default=None, max_length=300)
+    html: str | None = None
+    from_address: str | None = Field(default=None, max_length=320)
+
+
+class AdminInvitePreviewIn(BaseModel):
+    subject: str = Field(default="", max_length=300)
+    html: str = ""
+
+
+class AdminInvitePreviewOut(BaseModel):
+    subject: str
+    html: str
+
+
 class AdminMailTestIn(BaseModel):
     to: str = Field(min_length=3, max_length=320)