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.ts

@@ -58,3 +58,13 @@ export function offlinePreloadEligible(opts: {
 }): boolean {
   return opts.hasEmail && opts.standalone && !opts.inTelegram && !opts.inVK && opts.online;
 }
+
+/**
+ * shouldBootOffline decides whether a cold start skips the network and launches straight into
+ * offline mode: the deliberate offline flag is persisted-on AND a prior online session left a cached
+ * session and profile to start from. Without both (e.g. cleared storage, or a never-online install),
+ * the app must boot online once first — the caller then drops the sticky flag and continues online.
+ */
+export function shouldBootOffline(opts: { offlineActive: boolean; hasSession: boolean; hasProfile: boolean }): boolean {
+  return opts.offlineActive && opts.hasSession && opts.hasProfile;
+}