Wire SyncEngine into BrowserCore

Add per-profile sync orchestration to `ely_browser_core`:

- `SyncEngine::for_profile_dir` loads / generates the persistent
  device identity under `<profile_data>/sync/device.json` and reads
  the bearer token from `<profile_data>/sync/bearer.token`.
- `install_bearer` accepts (or clears) the Better Auth session
  token; everything else stays inert until a token is on disk.
- `upload_now(&BrowserCore)` serialises the user's bookmarks into a
  stable JSON snapshot, ships it via `SyncApiClient::upload_snapshot`,
  and remembers the resulting snapshot id / logical clock / device
  for the UI to surface.
- `BrowserCore::visible_bookmarks_for_sync` returns a read-only view
  the engine can iterate without touching the in-memory state.

The shell / settings-page wiring that calls `upload_now` ships
separately so this commit stays a pure model-layer change with no
runtime behaviour difference until the UI plugs in.

crates/ely_browser_core/Cargo.toml

@@ -7,6 +7,7 @@ rust-version.workspace = true
 
 [dependencies]
 ely_domain = { path = "../ely_domain" }
+ely_sync_client = { path = "../ely_sync_client" }
 serde.workspace = true
 serde_json.workspace = true
 thiserror.workspace = true