Settings Sync: consider recovery from transient authentication session lookup failures

Summary

Settings Sync can become stuck showing Sign in to Sync Settings after a transient authentication session lookup failure, even though the persisted account remains valid and a later lookup succeeds without interactive authentication.

This issue is split from #333975 so the Settings Sync owner can decide whether a scoped mitigation is appropriate. The parent issue tracks the more complete authentication-layer fix that would distinguish temporary token acquisition failures from genuinely absent or invalid sessions.

Current behavior

When the configured authentication provider temporarily returns no scoped sessions, Settings Sync clears its current in-memory account and changes the account status to Unavailable. No automatic retry occurs when connectivity returns, so the user is shown a sign-in prompt until another event—such as restarting the extension host—causes the session to be queried again.

Decision

Please evaluate whether Settings Sync should provide a local recovery path while the authentication-layer work in #333975 is unresolved, or whether this issue should be closed in favor of fixing the provider contract directly.

One possible mitigation would be a bounded retry when Sync still has a persisted session ID and has not received an explicit session-removal event. This is only a suggestion; the appropriate behavior and scope are left to the Settings Sync owner.

Related: #333975