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/migrations/versions/0027_invitations.py

@@ -0,0 +1,63 @@
+"""invitations: users invite friends, even while sign-up is closed
+
+An administrator switch lets every user send a few single-use invitation links
+by email; a link opens sign-up for the person it was sent to even when public
+registration is off. The email is built from a template the administrator
+uploads (or the built-in one) and sent from the instance's own address.
+
+Revision ID: 0027
+Revises: 0026
+Create Date: 2026-10-14
+"""
+
+from __future__ import annotations
+
+from collections.abc import Sequence
+
+from alembic import op
+
+revision: str = "0027"
+down_revision: str | None = "0026"
+branch_labels: str | Sequence[str] | None = None
+depends_on: str | Sequence[str] | None = None
+
+
+def upgrade() -> None:
+    op.execute(
+        """
+        ALTER TABLE app_settings
+          ADD COLUMN invitations_enabled boolean NOT NULL DEFAULT false,
+          ADD COLUMN invite_from text NOT NULL DEFAULT '',
+          ADD COLUMN invite_subject text NOT NULL DEFAULT '',
+          ADD COLUMN invite_template text NOT NULL DEFAULT ''
+        """
+    )
+    op.execute(
+        """
+        CREATE TABLE invitations (
+          id uuid PRIMARY KEY DEFAULT gen_random_uuid(),
+          inviter_id uuid NOT NULL REFERENCES users(id) ON DELETE CASCADE,
+          token_hash text NOT NULL UNIQUE,
+          invitee_name text NOT NULL,
+          invitee_email text NOT NULL,
+          created_at timestamptz NOT NULL DEFAULT now(),
+          expires_at timestamptz NOT NULL,
+          used_at timestamptz,
+          used_by uuid REFERENCES users(id) ON DELETE SET NULL
+        )
+        """
+    )
+    op.execute("CREATE INDEX ix_invitations_inviter ON invitations (inviter_id)")
+
+
+def downgrade() -> None:
+    op.execute("DROP TABLE IF EXISTS invitations")
+    op.execute(
+        """
+        ALTER TABLE app_settings
+          DROP COLUMN IF EXISTS invitations_enabled,
+          DROP COLUMN IF EXISTS invite_from,
+          DROP COLUMN IF EXISTS invite_subject,
+          DROP COLUMN IF EXISTS invite_template
+        """
+    )