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/offline.test.ts

@@ -1,5 +1,5 @@
 import { describe, it, expect, beforeEach } from 'vitest';
-import { loadOfflinePref, saveOfflinePref, offlineReady, missingDicts, offlinePreloadEligible } from './offline';
+import { loadOfflinePref, saveOfflinePref, offlineReady, missingDicts, offlinePreloadEligible, shouldBootOffline } from './offline';
 import type { Variant } from './model';
 
 // A minimal in-memory localStorage for the persistence tests (node has none).
@@ -45,4 +45,11 @@ describe('offline mode helpers', () => {
     expect(offlinePreloadEligible({ ...base, inVK: true })).toBe(false);
     expect(offlinePreloadEligible({ ...base, online: false })).toBe(false);
   });
+
+  it('shouldBootOffline requires the offline flag plus a cached session and profile', () => {
+    expect(shouldBootOffline({ offlineActive: true, hasSession: true, hasProfile: true })).toBe(true);
+    expect(shouldBootOffline({ offlineActive: false, hasSession: true, hasProfile: true })).toBe(false);
+    expect(shouldBootOffline({ offlineActive: true, hasSession: false, hasProfile: true })).toBe(false);
+    expect(shouldBootOffline({ offlineActive: true, hasSession: true, hasProfile: false })).toBe(false);
+  });
 });