Installable app, push notifications about new mail, Install app entry

The webmail is now a PWA: web app manifest, icons (any + maskable, a status-bar
badge), theme-coloured title bar following the chosen theme, and an app-icon
badge with the unread Inbox count. The service worker is always installed;
offline access is on only when it is registered as /sw.js?offline=1, so
turning it on or off is an update that applies at once.

Notifications (Settings → Accounts → Notifications, per device) use Web Push.
Encryption (RFC 8291) and VAPID signing (RFC 8292) are implemented in
app/push/webpush.py — pywebpush needs a newer cryptography than we pin — and
checked against the RFC's worked example. The server makes its key pair on
first use (private half encrypted with MASTER_KEY). New mail found by the live
sync in an Inbox enqueues a job 5 s later that tells the user's devices about
messages still unread there, under 2 hours old and not from the user; more
than three become one "N new messages". A subscription belongs to the session
it was made under: signed out or revoked, nothing more is sent there. Endpoints
are limited to the known push services (no SSRF). Nothing shows while the app
is in front (except on Apple, which requires it). Tested with real pushes
through Google's service in Chromium and Opera.

The mobile drawer gets "Install app": Chrome's own install dialog where the
browser offers one, else short steps for iPhone/iPad, Opera and Firefox, with
"Don't show this again". docs/nas-install.md §5.3 covers installing,
notifications, Public URL and a later Android app (TWA).

Migration 0022: push_subscriptions, app_settings.vapid_*.

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

backend/app/models.py

@@ -82,6 +82,11 @@ class AppSettings(Base):
     # Where users reach the app, e.g. https://mail.example.com — reset links are
     # built from this, never from the request's Host header.
     public_url: Mapped[str] = mapped_column(Text, nullable=False, server_default=text("''"))
+    # The key pair push notifications are signed with (VAPID, RFC 8292): made on
+    # first use; the private half vault-encrypted, the public half as browsers
+    # take it (base64url, uncompressed P-256 point).
+    vapid_public: Mapped[str] = mapped_column(Text, nullable=False, server_default=text("''"))
+    vapid_private_ct: Mapped[bytes | None] = mapped_column(BYTEA)
     updated_at: Mapped[dt.datetime] = _now()
 
 
@@ -344,6 +349,27 @@ class SavedSearch(Base):
     pinned: Mapped[bool] = mapped_column(nullable=False, server_default=text("true"))
 
 
+class PushSubscription(Base):
+    """A browser or installed app to tell about new mail (Web Push)."""
+
+    __tablename__ = "push_subscriptions"
+
+    id: Mapped[uuid.UUID] = _uuid_pk()
+    user_id: Mapped[uuid.UUID] = mapped_column(
+        UUID(as_uuid=True), ForeignKey("users.id", ondelete="CASCADE"), nullable=False, index=True
+    )
+    # The push service URL the browser handed out; posting to it reaches the device.
+    endpoint: Mapped[str] = mapped_column(Text, nullable=False, unique=True)
+    # The browser's keys the message is encrypted to (RFC 8291), base64url.
+    p256dh: Mapped[str] = mapped_column(Text, nullable=False)
+    auth: Mapped[str] = mapped_column(Text, nullable=False)
+    # The sign-in it was made under: nothing is sent once that session is gone.
+    session_sid: Mapped[str] = mapped_column(Text, nullable=False)
+    user_agent: Mapped[str] = mapped_column(Text, nullable=False, server_default=text("''"))
+    created_at: Mapped[dt.datetime] = _now()
+    last_used_at: Mapped[dt.datetime | None] = mapped_column(TIMESTAMP(timezone=True))
+
+
 class PluginKv(Base):
     """Namespaced key/value store for plugins (SPEC §11 ``plugin_kv``).