Reflect real sync state on the Sync settings page

`SyncConnectionState` was a one-variant enum (`SignedOut`), so the
Sync page rendered "Local-only · sign-in coming soon" even after the
bearer token landed on disk and the upload thread completed. The
state machine now mirrors the actual lifecycle.

What lands:
- `SyncConnectionState` gains `SignedIn`, `AwaitingDeviceApproval`,
  `SyncReady { last_synced_at_secs }`, `SyncError { message }`.
  `SyncObjectState::Synced` joins the per-object enum so individual
  rows can advertise "Synced" once a successful upload lands.
- `BrowserCore` stores the current `SyncConnectionState` and exposes
  `set_sync_connection_state`. `sync_status` now propagates the live
  state into the snapshot the UI reads.
- `ElyShell::probe_initial_sync_state` inspects
  `<profile_data>/sync/bearer.token` synchronously at construction
  so the first render of the sync page is honest about whether the
  user is signed in.
- A `std::sync::mpsc` channel ferries upload outcomes from the
  off-thread worker back to the shell; the existing 8 ms tick
  drains it and stamps `core.set_sync_connection_state` with the
  freshest result. The UI now shows "Signed in · awaiting first
  sync", "Synced · last upload Xm ago", "Sync error · …", and the
  worker-special "Signed in · waiting for device approval" when the
  server returns `device_not_approved`.

crates/ely_browser_core/src/state.rs

@@ -162,6 +162,7 @@ pub struct BrowserCore {
     update_policy: UpdatePolicy,
     appearance: AppearanceSettings,
     sync_object_policies: SyncObjectPolicies,
+    sync_connection_state: ely_domain::SyncConnectionState,
     command_query: String,
 }
 
@@ -210,6 +211,7 @@ impl BrowserCore {
             update_policy: UpdatePolicy::default(),
             appearance: AppearanceSettings::default(),
             sync_object_policies: SyncObjectPolicies::default(),
+            sync_connection_state: ely_domain::SyncConnectionState::SignedOut,
             spaces: vec![space],
             profiles: vec![profile],
             tabs: vec![tab],

crates/ely_browser_core/src/state/sync.rs

@@ -1,4 +1,7 @@
-use ely_domain::{SyncObjectKind, SyncObjectPolicy, SyncObjectState, SyncObjectStatus, SyncStatus};
+use ely_domain::{
+    SyncConnectionState, SyncObjectKind, SyncObjectPolicy, SyncObjectState, SyncObjectStatus,
+    SyncStatus,
+};
 
 use super::BrowserCore;
 
@@ -75,54 +78,57 @@ impl BrowserCore {
         self.sync_object_policies.get(kind)
     }
 
+    pub fn set_sync_connection_state(&mut self, state: SyncConnectionState) {
+        self.sync_connection_state = state;
+    }
+
     pub(super) fn sync_status(&self) -> SyncStatus {
-        SyncStatus::signed_out(vec![
-            self.sync_object_status(
-                SyncObjectKind::Spaces,
-                self.spaces.len(),
-                SyncObjectState::LocalOnly,
-            ),
-            self.sync_object_status(
-                SyncObjectKind::Tabs,
-                self.sync_enabled_tab_count(),
-                SyncObjectState::LocalOnly,
-            ),
-            self.sync_object_status(
-                SyncObjectKind::Bookmarks,
-                self.bookmarks.len(),
-                SyncObjectState::LocalOnly,
-            ),
-            self.sync_object_status(
-                SyncObjectKind::Notes,
-                self.notes.len(),
-                SyncObjectState::LocalOnly,
-            ),
-            self.sync_object_status(
-                SyncObjectKind::ReadingList,
-                self.reading_list.len(),
-                SyncObjectState::LocalOnly,
-            ),
-            self.sync_object_status(
-                SyncObjectKind::Profiles,
-                self.profiles.len(),
-                SyncObjectState::LocalOnly,
-            ),
-            self.sync_object_status(
-                SyncObjectKind::SitePermissions,
-                self.site_permissions.len(),
-                SyncObjectState::LocalOnly,
-            ),
-            self.sync_object_status(
-                SyncObjectKind::History,
-                self.history_entries.len(),
-                SyncObjectState::PrivacyControlled,
-            ),
-            self.sync_object_status(
-                SyncObjectKind::PluginSettings,
-                self.installed_plugins.len(),
-                SyncObjectState::LocalOnly,
-            ),
-        ])
+        let enabled_state = match &self.sync_connection_state {
+            SyncConnectionState::SyncReady { .. } => SyncObjectState::Synced,
+            _ => SyncObjectState::LocalOnly,
+        };
+        SyncStatus::new(
+            self.sync_connection_state.clone(),
+            vec![
+                self.sync_object_status(SyncObjectKind::Spaces, self.spaces.len(), enabled_state),
+                self.sync_object_status(
+                    SyncObjectKind::Tabs,
+                    self.sync_enabled_tab_count(),
+                    enabled_state,
+                ),
+                self.sync_object_status(
+                    SyncObjectKind::Bookmarks,
+                    self.bookmarks.len(),
+                    enabled_state,
+                ),
+                self.sync_object_status(SyncObjectKind::Notes, self.notes.len(), enabled_state),
+                self.sync_object_status(
+                    SyncObjectKind::ReadingList,
+                    self.reading_list.len(),
+                    enabled_state,
+                ),
+                self.sync_object_status(
+                    SyncObjectKind::Profiles,
+                    self.profiles.len(),
+                    enabled_state,
+                ),
+                self.sync_object_status(
+                    SyncObjectKind::SitePermissions,
+                    self.site_permissions.len(),
+                    enabled_state,
+                ),
+                self.sync_object_status(
+                    SyncObjectKind::History,
+                    self.history_entries.len(),
+                    SyncObjectState::PrivacyControlled,
+                ),
+                self.sync_object_status(
+                    SyncObjectKind::PluginSettings,
+                    self.installed_plugins.len(),
+                    enabled_state,
+                ),
+            ],
+        )
     }
 
     fn sync_object_status(