feat(navigation): persist last-port for next-login + root → /dashboard

Login routing previously always landed at the user's first port-role.
With a multi-port operator (super-admins, multi-tenant ops) the active
port reverted on every login, breaking the "I was working in X
yesterday" continuity.

- PortProvider PATCHes `/api/v1/me` with `preferences.defaultPortId =
  currentPort.id` whenever the active port changes (URL or explicit
  switch). Ref-keyed dedupe; fire-and-forget so navigation isn't
  blocked by a transient PATCH failure.
- UserMenu's port-switcher also writes the preference on click so the
  preference is captured even for users who never re-render through
  PortProvider.
- /dashboard resolver checks `preferences.defaultPortId` first, falling
  back to first-port-by-name (super-admin) or first-role (everyone
  else). The preference is verified against current access before being
  honoured — a stale id from a revoked role or archived port can't
  strand the user on a 403.
- Add /src/app/page.tsx that redirects `/` → `/dashboard` so the
  middleware's `redirect=/` post-login parameter doesn't dump users on
  an empty 404. The existing /dashboard handler then routes them on to
  their resolved port.
- UserMenu sign-out: replace `router.push('/api/auth/sign-out')` (which
  issued a GET against better-auth's POST-only endpoint, causing Safari
  and Comet/Arc to land the JSON response as a `sign_out` download)
  with `signOut()` from the auth client + an explicit redirect.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

src/app/page.tsx

@@ -0,0 +1,13 @@
+import { redirect } from 'next/navigation';
+
+/**
+ * Root `/` has no UI of its own — every authenticated surface lives under
+ * a port slug. Forward to `/dashboard`, which resolves the user's default
+ * port and redirects again to `/<portSlug>/dashboard`. Without this, a
+ * post-login redirect of `redirect=/` (set by middleware when the user
+ * originally hit `/`) lands on an empty 404.
+ */
+export default function RootPage() {
+  // eslint-disable-next-line @typescript-eslint/no-explicit-any
+  redirect('/dashboard' as any);
+}