fix(offline): cold-boot offline from the persisted session + profile

An installed PWA relaunched with the network off hung on the splash: C1's
precache served the shell, but bootstrap() adopted the session and fetched the
profile over the network, which hung. Persist the profile (on every online
adopt + refresh, cleared on logout) and short-circuit bootstrap when the
deliberate offline flag is sticky-on: with a cached session + profile, skip the
network and land straight in the offline lobby. Without a cached profile (never
online), drop the sticky flag and boot online — the first launch must be online.

- session.ts: saveProfile/loadProfile/clearProfile (mirror saveSession).
- offline.ts: shouldBootOffline decision (unit-tested).
- app.svelte.ts: persist in adoptSession + refreshProfile, clear on logout,
  the offline boot short-circuit in bootstrap.

Docs: ARCHITECTURE. Online cold-start unaffected (e2e 196); the offline boot is
contour-verified (the mock e2e cannot enter sticky-offline).

ui/src/lib/session.ts

@@ -3,7 +3,7 @@
 // re-login), with a localStorage fallback. Losing the store just means re-login —
 // acceptable, and for a guest it simply mints a fresh guest.
 
-import type { Session } from './model';
+import type { Session, Profile } from './model';
 import type { ThemePref } from './theme';
 import type { Locale } from './i18n/catalog';
 import type { BoardLabelMode } from './boardlabels';
@@ -119,6 +119,25 @@ export function clearSession(): Promise<void> {
   return kvDel(SESSION_KEY);
 }
 
+const PROFILE_KEY = 'profile';
+
+/** loadProfile reads the last persisted profile (or null). It backs the offline cold-boot: with no
+ *  network, bootstrap uses it instead of fetching a fresh one. */
+export function loadProfile(): Promise<Profile | null> {
+  return kvGet<Profile>(PROFILE_KEY);
+}
+
+/** saveProfile persists the caller's own profile so a later offline launch can start from it (its
+ *  variant preferences, dictionary versions and display name), best-effort. */
+export function saveProfile(p: Profile): Promise<void> {
+  return kvSet(PROFILE_KEY, p);
+}
+
+/** clearProfile drops the persisted profile (on logout, with the session). */
+export function clearProfile(): Promise<void> {
+  return kvDel(PROFILE_KEY);
+}
+
 export interface Prefs {
   theme: ThemePref;
   locale: Locale;